A373935 Number of compositions of 7*n-3 into parts 6 and 7.

0, 0, 1, 4, 10, 20, 35, 56, 85, 131, 231, 506, 1287, 3367, 8464, 20026, 44609, 94334, 191710, 380190, 748924, 1491735, 3044927, 6398259, 13770795, 30031820, 65615746, 142422743, 305750022, 648652029, 1362500345, 2843775112, 5922703731, 12356169575

Offset

1,4

Links

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

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-6,1).

Formula

a(n) = A017847(7*n-3).

a(n) = Sum_{k=0..floor(n/6)} binomial(n+k,n-3-6*k).

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 6*a(n-6) + a(n-7).

G.f.: x^3*(1-x)^3/((1-x)^7 - x^6).

a(n) = A373936(n+1)-A373936(n). - R. J. Mathar, Jun 24 2024

Prog

(PARI) a(n) = sum(k=0, n\6, binomial(n+k, n-3-6*k));

Crossrefs

Cf. A369809, A373912, A373933, A373934, A373936, A373937.

Cf. A017847.

Sequence in context: A000292 A352669 A101552 * A352210 A038419 A301208

Adjacent sequences: A373932 A373933 A373934 * A373936 A373937 A373938

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 23 2024

Status

approved