A027797 a(n) = 22*(n+1)*binomial(n+3,12).

220, 3146, 24024, 130130, 560560, 2042040, 6534528, 18845112, 49884120, 122862740, 284524240, 624660036, 1308811504, 2631351800, 5099265600, 9561123000, 17401243860, 30826185390, 53279826600, 90034894950, 149023274400, 241985412240, 386041244160, 605812006800

Offset

9,1

Comments

Number of 16-subsequences of [ 1, n ] with just 3 contiguous pairs.

Links

T. D. Noe, Table of n, a(n) for n = 9..1000

Index entries for linear recurrences with constant coefficients, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).

Formula

G.f.: 22*(10+3x)*x^9/(1-x)^14.

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

From Amiram Eldar, Feb 02 2022: (Start)

Sum_{n>=9} 1/a(n) = 632045299/12806640 - 5*Pi^2.

Sum_{n>=9} (-1)^(n+1)/a(n) = 5*Pi^2/2 + 96256*log(2)/231 - 4014869821/12806640. (End)

Mathematica

Table[22 (n + 1) Binomial[n + 3, 12], {n, 9, 32}] (* or *) Table[Binomial[n + 1, 10] Binomial[n + 3, 3], {n, 9, 32}] (* Michael De Vlieger, Mar 16 2016 *)

Crossrefs

Sequence in context: A211820 A215491 A258537 * A055663 A333139 A022042

Adjacent sequences: A027794 A027795 A027796 * A027798 A027799 A027800

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved