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

0,2

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).

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.

Mathematica

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

Prog

(Magma) [(2/3)*n*(n+1)*(n+2)+(-1)^n: n in [0..35]];
(PARI) for(n=0, 35, print1((2/3)*n*(n+1)*(n+2)+(-1)^n", "));

Crossrefs

Cf. A005744, A026035, A175109, A131941.

Sequence in context: A354475 A073162 A146186 * A196781 A298232 A340463

Adjacent sequences: A179780 A179781 A179782 * A179784 A179785 A179786

Keyword

nonn,easy

Author

Bruno Berselli, Jul 29 2010 - Sep 07 2010

Status

approved