1,4

Also number of partitions of n-1 with a distinguished part different from all the others. [Comment corrected by Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 13 2008]

In general the number of times that j appears in the partitions of n equals Sum_{k<n, k = n (mod j)} P(k). In particular this gives a formula for a(n), A024787, ..., A024794, for j = 2,...,10; it generalizes the formula given for A000070 for j=1. - Jose Luis Arregui (arregui(AT)posta.unizar.es), Apr 05 2002

Equals row sums of triangle A173238 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 13 2010]

J. Riordan, Combinatorial Identities, Wiley, 1968, p. 184.

E. Deutsch et al., Problem 11237, Amer. Math. Monthly, 115 (No. 7, 2008), 666-667. [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 13 2008]

a(n) = sum{k=1 to floor(n/2)} A000041(n-2k).

a(n) = Sum_{k<n, k = n (mod 2)} P(k), P(k) =number of partitions of k as in A000041, P(0) = 1. - Jose Luis Arregui (arregui(AT)posta.unizar.es), Apr 05 2002

G.f.: x/((1-x)*(1-x^2)^2))*product(1/(1-x^j), j=3..infty) from Riordan reference second term, last eq.

<< DiscreteMath`Combinatorica`; Table[ Count[ Flatten[ Partitions[n]], 2], {n, 1, 50} ]

Cf. A066633, A024787, A024788, A024789, A024790, A024791, A024792, A024793, A024794.

Column 2 of A060244.

First differences of A000097.

Sequence in context: A099108 A001994 A084421 this_sequence A097497 A006167 A137504

Adjacent sequences: A024783 A024784 A024785 this_sequence A024787 A024788 A024789

Cf. A173238 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 13 2010]

nonn

Clark Kimberling (ck6(AT)evansville.edu)

Formula and comment from Christian G. Bower (bowerc(AT)usa.net), Jun 22 2000