A027794 a(n) = 12*(n+1)*binomial(n+3,9).

84, 960, 5940, 26400, 94380, 288288, 780780, 1921920, 4375800, 9335040, 18845112, 36279360, 67016040, 119380800, 205931880, 345181056, 563861100, 899870400, 1406047500, 2154952800, 3244861620, 4807202400, 7015706100, 10097568000, 14346961200, 20141282304

Offset

6,1

Comments

Number of 13-subsequences of [ 1, n ] with just 3 contiguous pairs.

Links

T. D. Noe, Table of n, a(n) for n = 6..1000

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Formula

G.f.: 12*(7+3x)*x^6/(1-x)^11.

a(n) = C(n+1, 7)*C(n+3, 3) - Zerinvary Lajos, May 10 2005; corrected by R. J. Mathar, Mar 16 2016

From Amiram Eldar, Feb 01 2022: (Start)

Sum_{n>=6} 1/a(n) = 7*Pi^2/2 - 386741/11200.

Sum_{n>=6} (-1)^n/a(n) = 7*Pi^2/4 + 512*log(2)/5 - 2964833/33600. (End)

Mathematica

Table[12 (n + 1) Binomial[n + 3, 9], {n, 6, 31}] (* or *) Table[Binomial[n + 1, 7] Binomial[n + 3, 3], {n, 6, 31}] (* Michael De Vlieger, Mar 16 2016 *)

Crossrefs

Sequence in context: A069080 A219577 A093284 * A219713 A027821 A220049

Adjacent sequences: A027791 A027792 A027793 * A027795 A027796 A027797

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved