A027790 a(n) = 10*(n+1)*binomial(n+3,5)/3.

10, 80, 350, 1120, 2940, 6720, 13860, 26400, 47190, 80080, 130130, 203840, 309400, 456960, 658920, 930240, 1288770, 1755600, 2355430, 3116960, 4073300, 5262400, 6727500, 8517600, 10687950, 13300560, 16424730, 20137600

Offset

2,1

Links

Table of n, a(n) for n=2..29.

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

Formula

Number of 9-subsequences of [ 1, n ] with just 3 contiguous pairs.

G.f.: 10*(1+x)*x^2/(1-x)^7.

a(n) = binomial(n+1, 3)*binomial(n+3, 3) = A000292(n-1)*A000292(n+1). - Zerinvary Lajos, May 13 2005

a(n) = 10*A040977(n). - R. J. Mathar, May 22 2013

From Amiram Eldar, Jan 06 2021: (Start)

Sum_{n>=2} 1/a(n) = 3*Pi^2/2 - 235/16.

Sum_{n>=2} (-1)^n/a(n) = 3*Pi^2/4 - 117/16. (End)

Mathematica

Table[10(n+1) Binomial[n+3, 5]/3, {n, 2, 30}] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {10, 80, 350, 1120, 2940, 6720, 13860}, 30] (* Harvey P. Dale, Jan 15 2015 *)

Crossrefs

Cf. A000292, A040977.

Sequence in context: A206764 A253649 A244729 * A000575 A220485 A055285

Adjacent sequences: A027787 A027788 A027789 * A027791 A027792 A027793

Keyword

nonn,easy

Author

thi ngoc dinh (via R. K. Guy)

Status

approved