A179783 a(n) = 2*n*(n+1)*(n+2)/3 + (-1)^n.

1, 3, 17, 39, 81, 139, 225, 335, 481, 659, 881, 1143, 1457, 1819, 2241, 2719, 3265, 3875, 4561, 5319, 6161, 7083, 8097, 9199, 10401, 11699, 13105, 14615, 16241, 17979, 19841, 21823, 23937, 26179, 28561, 31079

Offset: 0

Author

Bruno Berselli, Jul 29 2010 - Sep 07 2010

Keywords

• nonn
• easy

Comments

First differences in 2*A081352.

Second differences in 4*A004442.

Links

• B. Berselli, Table of n, a(n) for n = 0..10000.
• Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).

Crossrefs

Cf. A005744, A026035, A175109, A131941.

Programs

Magma

[(2/3)*n*(n+1)*(n+2)+(-1)^n: n in [0..35]];

Mathematica

LinearRecurrence[{3,-2,-2,3,-1},{1,3,17,39,81},40] (* Harvey P. Dale, Mar 04 2023 *)

PARI

for(n=0, 35, print1((2/3)*n*(n+1)*(n+2)+(-1)^n", "));

Formula

G.f.: (1+10*x^2-4*x^3+x^4)/((1+x)*(1-x)^4); exp(-x)+(2/3)*exp(x)*x*(6+6*x+x^2).

a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5) for n>4.

a(n) = 4*A000292(n)+(-1)^n.