A245581 a(n) = (5 * (1 + (-1)^(1 + n)) + 2 * n^2) / 4.

0, 3, 2, 7, 8, 15, 18, 27, 32, 43, 50, 63, 72, 87, 98, 115, 128, 147, 162, 183, 200, 223, 242, 267, 288, 315, 338, 367, 392, 423, 450, 483, 512, 547, 578, 615, 648, 687, 722, 763, 800, 843, 882, 927, 968, 1015, 1058, 1107, 1152, 1203, 1250, 1303, 1352, 1407

Offset: 0

Author

Peter Luschny, Jul 26 2014

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Crossrefs

Cf. A097080, A209350, A245578.

Programs

Magma

[(5*(1+(-1)^(1+n))+2*n^2) / 4: n in [0..60]]; // Vincenzo Librandi, Jul 27 2014

Maple

A245581 := n -> (5*(1+(-1)^(1+n))+2*n^2)/4; seq(A245581(n), n=0..53);

Mathematica

CoefficientList[Series[-x (3 x^2 - 4 x + 3)/((x - 1)^3 (x + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 27 2014 *)

PARI

concat(0, Vec(-x*(3*x^2-4*x+3)/((x-1)^3*(x+1)) + O(x^100))) \\ Colin Barker, Jul 26 2014

Sage

def A():
    a, b, c, d = 0, 3, 2, 7
    while True:
        yield a
        a, b, c, d = b, c, d, a + 2*(d - b)
A245581 = A(); [next(A245581) for n in range(54)]

Formula

a(n) = a(-n).

a(2*n+1) = A097080(n+1).

a(2*n+6) = A245578(2*n+4) = 2*A209350(2*n+4).

a(n) = 2*a(n-1)-2*a(n-3)+a(n-4). - Colin Barker, Jul 26 2014

G.f.: -x*(3*x^2-4*x+3) / ((x-1)^3*(x+1)). - Colin Barker, Jul 26 2014

E.g.f.: (exp(x)*x*(x+1) + 5*sinh(x))/2. - Peter Luschny, Aug 04 2014