A373961 Number of compositions of 6*n-1 into parts 5 and 6.

1, 2, 3, 4, 5, 7, 15, 44, 129, 340, 804, 1742, 3550, 7009, 13835, 28033, 58993, 128136, 282569, 622575, 1357136, 2918449, 6204578, 13104675, 27646776, 58502733, 124411595, 265807567, 569552644, 1221316021, 2616456236, 5595314908, 11944318042, 25466629978

Offset: 1

Author

Seiichi Manyama, Jun 23 2024

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A107025, A369794, A373962, A373963, A373964.

Cf. A017837.

Programs

PARI

a(n) = sum(k=0, n\5, binomial(n+k, n-1-5*k));

Formula

a(n) = A017837(6*n-1).

a(n) = Sum_{k=0..floor(n/5)} binomial(n+k,n-1-5*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*(1-x)^4/((1-x)^6 - x^5).

a(n) = A373962(n+1) - A373962(n).