A371125 - OEIS

A371125

Number of compositions of 6*n into parts 1 and 6.

1, 2, 9, 43, 196, 882, 3970, 17887, 80608, 363254, 1636944, 7376591, 33241289, 149795989, 675029164, 3041899638, 13707783053, 61771701389, 278363253873, 1254394801761, 5652708454881, 25472931513057, 114789263420590, 517277526141329, 2331019740675071

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (7,-15,20,-15,6,-1).

FORMULA

a(n) = A005708(6*n).

a(n) = Sum_{k=0..n} binomial(n+5*k,n-k).

a(n) = 7*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).

G.f.: 1/(1 - x - x/(1 - x)^5).

PROG

(PARI) a(n) = sum(k=0, n, binomial(n+5*k, n-k));

CROSSREFS

Cf. A052544, A055988, A369836, A373907, A373890.

Cf. A107025, A373904, A373905, A373906.

Cf. A005708.

Sequence in context: A275620 A121365 A018960 * A217666 A002310 A309986

Adjacent sequences: A371122 A371123 A371124 * A371126 A371127 A371128

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Jun 22 2024

STATUS

approved

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