A373934 Number of compositions of 7*n-2 into parts 6 and 7.

0, 1, 3, 6, 10, 15, 21, 29, 46, 100, 275, 781, 2080, 5097, 11562, 24583, 49725, 97376, 188480, 368734, 742811, 1553192, 3353332, 7372536, 16261025, 35583926, 76806997, 163327279, 342902007, 713848316, 1481274767, 3078928619, 6433465844, 13534471164

Offset

1,3

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-2).

a(n) = Sum_{k=0..floor(n/6)} binomial(n+k,n-2-6*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^2*(1-x)^4/((1-x)^7 - x^6).

a(n) = A373935(n+1)-A373935(n). - R. J. Mathar, Jun 24 2024

Prog

(PARI) a(n) = sum(k=0, n\6, binomial(n+k, n-2-6*k));

Crossrefs

Cf. A369809, A373912, A373933, A373935, A373936, A373937.

Cf. A017847, A369850.

Sequence in context: A101551 A227430 A051166 * A188278 A188279 A365699

Adjacent sequences: A373931 A373932 A373933 * A373935 A373936 A373937

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 23 2024

Status

approved