A340326 a(n) = a(n-2) + (-1)^n*a(n-1) + n*(1-(-1)^n) with a(0) = a(1) = 1.

1, 1, 2, 5, 7, 8, 15, 7, 22, 3, 25, 0, 25, 1, 26, 5, 31, 8, 39, 7, 46, 3, 49, 0, 49, 1, 50, 5, 55, 8, 63, 7, 70, 3, 73, 0, 73, 1, 74, 5, 79, 8, 87, 7, 94, 3, 97, 0, 97, 1, 98, 5, 103, 8, 111, 7, 118, 3, 121, 0, 121, 1, 122, 5, 127, 8, 135, 7, 142, 3, 145, 0, 145, 1, 146, 5, 151

Offset: 0

Author

José María Grau Ribas, Feb 07 2021

Keywords

• nonn
• easy

Comments

If n > 0 then a(2n-1) = A021067(n).

a(n) = 0 if and only if n == -1 (mod 12).

Links

• Index entries for linear recurrences with constant coefficients, signature (0,3,0,-4,0,3,0,-1).

Crossrefs

Cf. A030119, A065220.

Programs

Mathematica

a[0] = 1; a[1] = 1; a[n_] := a[n] =  a[n - 2] + (-1)^n a[n - 1] + n (1 - (-1)^n); Array[a,100]

Formula

G.f.: -(x^6+3*x^5-5*x^4-2*x^3+x^2-x-1)/(x^8-3*x^6+4*x^4-3*x^2+1). - Alois P. Heinz, Feb 07 2021