A027791 a(n) = 5*(n+1)*binomial(n+3,6).

20, 175, 840, 2940, 8400, 20790, 46200, 94380, 180180, 325325, 560560, 928200, 1485120, 2306220, 3488400, 5155080, 7461300, 10599435, 14805560, 20366500, 27627600, 37001250, 48976200, 64127700, 83128500, 106760745, 135928800, 171673040, 215184640, 267821400

Offset

3,1

Comments

Number of 10-subsequences of [ 1, n ] with just 3 contiguous pairs.

Links

Harvey P. Dale, Table of n, a(n) for n = 3..1000

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

G.f.: 5*(4+3x)*x^3/(1-x)^8.

a(n) = C(n+1, 4)*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>=3} 1/a(n) = 5939/300 - 2*Pi^2.

Sum_{n>=3} (-1)^(n+1)/a(n) = Pi^2 + 64*log(2)/5 - 5609/300. (End)

Mathematica

Table[5(n+1)Binomial[n+3, 6], {n, 3, 30}] (* or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {20, 175, 840, 2940, 8400, 20790, 46200, 94380}, 30] (* Harvey P. Dale, Nov 24 2015 *)

Crossrefs

Sequence in context: A022712 A359718 A056128 * A047819 A163689 A342387

Adjacent sequences: A027788 A027789 A027790 * A027792 A027793 A027794

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved