A373964 - OEIS

A373964

Number of compositions of 6*n-4 into parts 5 and 6.

0, 0, 0, 1, 5, 15, 35, 70, 127, 221, 396, 781, 1716, 4005, 9390, 21421, 47107, 100283, 208982, 432197, 898064, 1889152, 4028036, 8671852, 18739049, 40434205, 86861995, 185669195, 395358538, 840341619, 1786426005, 3803164340, 8111872645, 17329007156

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OFFSET

1,5

LINKS

Table of n, a(n) for n=1..34.

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

FORMULA

a(n) = A017837(6*n-4).

a(n) = Sum_{k=0..floor(n/5)} binomial(n+k,n-4-5*k).

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

G.f.: x^4*(1-x)/((1-x)^6 - x^5).

a(n) = A369794(n+1) - A369794(n).

MATHEMATICA

LinearRecurrence[{6, -15, 20, -15, 7, -1}, {0, 0, 0, 1, 5, 15}, 40] (* Harvey P. Dale, Dec 17 2025 *)

PROG

(PARI) a(n) = sum(k=0, n\5, binomial(n+k, n-4-5*k));

CROSSREFS

Cf. A107025, A369794, A373961, A373962, A373963.

Cf. A017837.

Sequence in context: A049016 A139761 A360047 * A275935 A137360 A195760

Adjacent sequences: A373961 A373962 A373963 * A373965 A373966 A373967

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Jun 24 2024

STATUS

approved