A373937 Number of compositions of 7*n-5 into parts 6 and 7.

0, 0, 0, 0, 1, 6, 21, 56, 126, 252, 463, 805, 1378, 2457, 4823, 10556, 24753, 58976, 137808, 310974, 675850, 1420916, 2914906, 5900631, 11931283, 24360194, 50559900, 106791426, 228638698, 492908713, 1062928750, 2281600816, 4862773227, 10287720750

Offset

1,6

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-5).

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

a(n) = A369809(n+1)-A369809(n). - R. J. Mathar, Jun 24 2024

Mathematica

LinearRecurrence[{7, -21, 35, -35, 21, -6, 1}, {0, 0, 0, 0, 1, 6, 21}, 40] (* Harvey P. Dale, Mar 20 2026 *)

Prog

(PARI) a(n) = sum(k=0, n\6, binomial(n+k, n-5-6*k));

Crossrefs

Cf. A369809, A373912, A373933, A373934, A373935, A373936.

Cf. A017847, A369808.

Sequence in context: A006090 A192080 A290993 * A275936 A375165 A019500

Adjacent sequences: A373934 A373935 A373936 * A373938 A373939 A373940

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 23 2024

Status

approved