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A383620

Number of weak compositions of n such that the set of adjacent differences is a subset of {-1,1}.

1, 4, 5, 9, 13, 20, 30, 45, 66, 102, 152, 229, 344, 518, 780, 1180, 1775, 2676, 4037, 6088, 9182, 13852, 20891, 31512, 47536, 71706, 108166, 163172, 246140, 371303, 560118, 844943, 1274606, 1922767, 2900522, 4375493, 6600511, 9956990, 15020307, 22658428

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OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..5598

EXAMPLE

a(0) = 1: (0).

a(1) = 4: (0,1), (0,1,0), (1,0), (1).

...

a(4) = 13: (0,1,0,1,0,1,0,1), (0,1,0,1,0,1,0,1,0), (1,0,1,0,1,0,1,0), (1,0,1,0,1,0,1), (0,1,0,1,2), (1,0,1,2), (2,1,0,1,0), (2,1,0,1), (0,1,2,1,0), (0,1,2,1), (1,2,1,0), (1,2,1), (4).

PROG

(PARI)

M(k) = matrix(k+1, k+1, i, j, if(i==j, 1, if(i==j-1, -x^(i-1), if(i==j+1, -x^(i-1), 0))))

A_x(N) = {my(k=N+1, x='x+O('x^k)); Vec(vecsum(M(k)^(-1) * vector(k+1, i, x^(i-1))~))}

A_x(10)

CROSSREFS

Cf. A007318, A173258, A214247, A214249, A227310.

Sequence in context: A363282 A116045 A096818 * A282467 A318980 A226622

Adjacent sequences: A383617 A383618 A383619 * A383621 A383622 A383623

KEYWORD

nonn

AUTHOR

John Tyler Rascoe, May 02 2025

STATUS

approved

URL: https://oeis.org/A383620

⇱ A383620 - OEIS