A373420 - OEIS

A373420

Number of Carlitz compositions of n (see A003242) such that the first and last parts are equal.

1, 1, 1, 1, 2, 3, 2, 7, 11, 17, 26, 54, 86, 155, 272, 464, 816, 1447, 2507, 4400, 7706, 13456, 23570, 41293, 72212, 126394, 221282, 387219, 677714, 1186311, 2076170, 3633761, 6360219, 11131698, 19483066, 34100455, 59683664, 104460655, 182832044, 319999739

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,5

LINKS

Table of n, a(n) for n=0..39.

FORMULA

G.f.: 1 + Sum_{i>0} (x^i)*(C(x)*(x^i) + x^i + 1)/(1+x^i)^2 where C(x) is the g.f. for A003242.

EXAMPLE

a(7) = 7 counts: (1,2,1,2,1), (1,2,3,1), (1,3,2,1), (1,5,1), (2,3,2), (3,1,3), and (7).

PROG

(PARI)

C_x(N) = {my(g=1/(1-sum(k=1, N, x^k/(1+x^k)))); g}