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Search: id:A105474
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| A105474 |
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Triangle read by rows: T(n,k) is number of compositions of n into k parts when each odd part can be of two kinds. |
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+0
2
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| 2, 1, 4, 2, 4, 8, 1, 9, 12, 16, 2, 8, 30, 32, 32, 1, 14, 37, 88, 80, 64, 2, 12, 66, 136, 240, 192, 128, 1, 19, 75, 257, 440, 624, 448, 256, 2, 16, 116, 352, 890, 1312, 1568, 1024, 512, 1, 24, 126, 564, 1401, 2844, 3696, 3840, 2304, 1024, 2, 20, 180, 720, 2370, 5004
(list; table; graph; listen)
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OFFSET
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1,1
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FORMULA
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G.f.=tz(2+z)/(1-2tz-z^2-tz^2).
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EXAMPLE
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T(4,2)=9 because we have (1,3),(1',3),(1,3'),(1',3'),(3,1),(3',1),(3,1'),(3',1') and (2,2).
Triangle begins:
2;
1,4;
2,4,8;
1,9,12,16;
2,8,30,32,32;
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MAPLE
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G:=t*z*(2+z)/(1-2*t*z-z^2-t*z^2): Gser:=simplify(series(G, z=0, 14)): for n from 1 to 12 do P[n]:=sort(coeff(Gser, z^n)) od: for n from 1 to 12 do seq(coeff(P[n], t^k), k=1..n) od; # yields sequence in triangular form
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CROSSREFS
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Row sums yield A052945.
Sequence in context: A065295 A035685 A118736 this_sequence A120988 A095979 A054269
Adjacent sequences: A105471 A105472 A105473 this_sequence A105475 A105476 A105477
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KEYWORD
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nonn,tabl
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 09 2005
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