A373912 Number of compositions of 7*n into parts 6 and 7.

1, 1, 1, 1, 1, 1, 2, 9, 37, 121, 331, 793, 1718, 3448, 6556, 12121, 22509, 43453, 89150, 193823, 436304, 989759, 2219064, 4869285, 10434412, 21900170, 45297211, 93054446, 191371581, 396480142, 830227401, 1756883373, 3746468095, 8017653633, 17151612398

Offset

0,7

Links

Table of n, a(n) for n=0..34.

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

Formula

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

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

Prog

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

Crossrefs

Cf. A373907, A373908, A373909, A373910, A373911.

Cf. A099099, A099131, A107025, A373913.

Cf. A017847.

Sequence in context: A306721 A306852 A275425 * A212386 A333883 A373911

Adjacent sequences: A373909 A373910 A373911 * A373913 A373914 A373915

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 22 2024

Status

approved