A213042 Convolution of (1,0,2,0,3,0,...) and (1,0,0,2,0,0,3,0,0,...); i.e., (A027656(n)) and (A175676(n+2)).

1, 0, 2, 2, 3, 4, 7, 6, 11, 12, 15, 18, 24, 24, 33, 36, 42, 48, 58, 60, 74, 80, 90, 100, 115, 120, 140, 150, 165, 180, 201, 210, 237, 252, 273, 294, 322, 336, 371, 392, 420, 448, 484, 504, 548, 576, 612, 648, 693, 720, 774, 810, 855, 900, 955, 990, 1055

Offset

0,3

Links

Table of n, a(n) for n=0..56.

Index entries for linear recurrences with constant coefficients, signature (0,2,2,-1,-4,-1,2,2,0,-1).

Formula

a(n) = 2*a(n-2)+2*a(n-3)-a(n-4)-4*a(n-5)-a(n-6)+2*a(n-7)+2*a(n-8)-a(n-10).

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

Example

a(6) = (1,0,2,0,3,0,4)**(1,0,0,2,0,0,3) = 1*3 + 0*0 + 2*0 + 0*2 + 3*0 + 0*0 + 4*1 = 7.

Mathematica

s = Normal[Series[1/((1 - x^2)^2 (1 - x^3)^2),
{x, 0, 80}]]
c = CoefficientList[s, t]  (* A213042 *)

Crossrefs

Sequence in context: A343399 A332106 A088633 * A114952 A328789 A086969

Adjacent sequences: A213039 A213040 A213041 * A213043 A213044 A213045

Keyword

nonn,easy

Author

Clark Kimberling, Jun 10 2012

Status

approved