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

Offset: 1

Author

Seiichi Manyama, Jun 24 2024

Keywords

• nonn
• easy

Links

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

Crossrefs

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

Cf. A017837.

Programs

PARI

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

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).