A373933 Number of compositions of 7*n-1 into parts 6 and 7.

1, 2, 3, 4, 5, 6, 8, 17, 54, 175, 506, 1299, 3017, 6465, 13021, 25142, 47651, 91104, 180254, 374077, 810381, 1800140, 4019204, 8888489, 19322901, 41223071, 86520282, 179574728, 370946309, 767426451, 1597653852, 3354537225, 7101005320, 15118658953

Offset

1,2

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-1).

a(n) = Sum_{k=0..floor(n/6)} binomial(n+k,n-1-6*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*(1-x)^5/((1-x)^7 - x^6).

a(n) = A373934(n+1)-A373934(n). - R. J. Mathar, Jun 24 2024

Prog

(PARI) a(n) = sum(k=0, n\6, binomial(n+k, n-1-6*k));

Crossrefs

Cf. A369809, A373912, A373934, A373935, A373936, A373937.

Cf. A017847, A369849.

Sequence in context: A119336 A133706 A081710 * A364455 A358175 A241947

Adjacent sequences: A373930 A373931 A373932 * A373934 A373935 A373936

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 23 2024

Status

approved