|
Search: id:A027383
|
|
|
| A027383 |
|
Number of balanced strings of length n: let d(S)= #(1)'s in S - #(0)'s, then S is balanced if every substring T has -2<=d(T)<=2. |
|
+0
21
|
|
| 1, 2, 4, 6, 10, 14, 22, 30, 46, 62, 94, 126, 190, 254, 382, 510, 766, 1022, 1534, 2046, 3070, 4094, 6142, 8190, 12286, 16382, 24574, 32766, 49150, 65534, 98302, 131070, 196606, 262142, 393214, 524286, 786430, 1048574, 1572862, 2097150, 3145726
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Number of "fold lines" seen when a rectangular piece of paper is folded n+1 times along alternate orthogonal directions and then unfolded - Quim Castellsaguer (qcastell(AT)pie.xtec.es), Dec 30 1999.
Also the number of binary strings with the property that, when scanning from left to right, once the first 1 is seen in position j, there must be a 1 in positions j+2, j+4, ... until the end of the string. (Positions j+1, j+3, ... can be occupied by 0 or 1.). - Jeffrey Shallit (shallit(AT)graceland.uwaterloo.ca), Sep 02 2002
Lower bound on number of vertices of (3,g)-cage, see A000066. - Eric Weisstein, May 20 2003
a(n) = sum 2^min(k,n-k), k=0..n
Partial sums of A016116. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 15 2007
Equals row sums of triangle A152201 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 29 2008]
|
|
REFERENCES
|
Under misprinted head B3 in Amer Math. Monthly, 104(1997) 753-754.
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Cage Graph
Index entries for sequences obtained by enumerating foldings
|
|
FORMULA
|
a_{2n} = 3 * 2^n - 2, a_{2n-1} = 2^{n+1} - 2. a_{n+2} = 2 * a_n + 2
2^Floor[(n+2)/2]+2^Floor[(n+1)/2]-2. - Quim Castellsaguer (qcastell(AT)pie.xtec.es).
a(n)=2^(n/2)(3+2sqrt(2)+(3-2sqrt(2))(-1)^n)/2-2. - Paul Barry (pbarry(AT)wit.ie), Apr 23 2004
a(n)=2^(n/2)(3+2sqrt(2)+(3-2sqrt(2))(-1)^n)/2-2 - Karl D'Souza (karl.dsouza(AT)abaqus.com), Jun 01 2005
a(n) = A132340(A052955(n)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 20 2007
a(n)=A052955(n+1)-1. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 15 2007
a(n)=A132666(a(n+1))-1. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 15 2007
a(n)=A132666(a(n-1)+1) for n>0. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 15 2007
A132666(a(n))=a(n-1)+1 for n>0 - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 15 2007
G.f.: (1 + x)/((1 - x)*(1 - 2*x^2)). - David Callan (callan(AT)stat.wisc.edu), Jul 22 2008
|
|
EXAMPLE
|
After 3 folds one sees 4 fold lines.
Example: a(3) = 6 because the strings 001, 010, 100, 011, 101, 110 have the property.
|
|
MAPLE
|
a[0]:=0:a[1]:=1:for n from 2 to 100 do a[n]:=2*a[n-2]+2 od: seq(a[n], n=1..41); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 16 2008
|
|
CROSSREFS
|
Cf. A132666.
A152201 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 29 2008]
Sequence in context: A001747 A048670 A077625 this_sequence A138016 A113118 A032417
Adjacent sequences: A027380 A027381 A027382 this_sequence A027384 A027385 A027386
|
|
KEYWORD
|
nonn,nice,easy
|
|
AUTHOR
|
R. K. Guy (rkg(AT)cpsc.ucalgary.ca)
|
|
EXTENSIONS
|
More terms from Larry Reeves (larryr(AT)acm.org), Mar 24 2000
|
|
|
Search completed in 0.003 seconds
|
