A027777 a(n) = 2*(n+1)*binomial(n+2,4).

6, 40, 150, 420, 980, 2016, 3780, 6600, 10890, 17160, 26026, 38220, 54600, 76160, 104040, 139536, 184110, 239400, 307230, 389620, 488796, 607200, 747500, 912600, 1105650, 1330056, 1589490, 1887900, 2229520, 2618880, 3060816, 3560480, 4123350, 4755240, 5462310

Offset: 2

Author

Thi Ngoc Dinh (via R. K. Guy)

Keywords

• nonn
• easy

Comments

Number of 7-subsequences of [ 1, n ] with just 2 contiguous pairs.

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Equals second right hand column of A163934. - Johannes W. Meijer, Oct 16 2009

Cf. A006411.

Programs

Mathematica

Table[2(n+1)Binomial[n+2,4],{n,2,35}]  (* Harvey P. Dale, Feb 03 2011 *)

Formula

G.f.: 2*(3+2x)*x^2/(1-x)^6.

a(n) = 2*A006411(n+1).

a(n) = C(n+1, 3)*C(n+2, 2) - Zerinvary Lajos, May 13 2005, corrected by R. J. Mathar, Feb 13 2016

From Amiram Eldar, Jan 28 2022: (Start)

Sum_{n>=2} 1/a(n) = Pi^2 - 29/3.

Sum_{n>=2} (-1)^n/a(n) = Pi^2/2 + 8*log(2) - 31/3. (End)