A373932 Number of compositions of 7*n-6 into parts 1 and 7.

1, 3, 13, 66, 330, 1624, 7973, 39173, 192539, 946375, 4651541, 22862658, 112371609, 552314945, 2714670141, 13342810843, 65580931949, 322335276473, 1584302440665, 7786967198052, 38273537040452, 188117350476413, 924611109563490, 4544534046237850

Offset

1,2

Links

Table of n, a(n) for n=1..24.

Index entries for linear recurrences with constant coefficients, signature (8,-21,35,-35,21,-7,1).

Formula

a(n) = A005709(7*n-6).

a(n) = Sum_{k=0..n} binomial(n+6*k,n-1-k).

a(n) = 8*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).

G.f.: x*(1-x)^5/((1-x)^7 - x).

a(n) = n*hypergeom([1-n,(1+n)/6,(2+n)/6, (3+n)/6, (4+n)/6, (5+n)/6, 1+n/6], [2/7, 3/7, 4/7, 5/7, 6/7, 8/7], -6^6/7^7). - Stefano Spezia, Jun 23 2024

Mathematica

a[n_]:=n*HypergeometricPFQ[{1-n, (1+n)/6, (2+n)/6, (3+n)/6, (4+n)/6, (5+n)/6, 1+n/6}, {2/7, 3/7, 4/7, 5/7, 6/7, 8/7}, -6^6/7^7]; Array[a, 24] (* Stefano Spezia, Jun 23 2024 *)

Prog

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

Crossrefs

Cf. A099253, A373907, A373928, A373929, A373930, A373931.

Cf. A005709.

Sequence in context: A198663 A156181 A260783 * A228987 A112807 A219537

Adjacent sequences: A373929 A373930 A373931 * A373933 A373934 A373935

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 23 2024

Status

approved