A191830 Expansion of x^2*(2-3*x)/(1-x-x^2)^2.

0, 0, 2, 1, 4, 5, 10, 16, 28, 47, 80, 135, 228, 384, 646, 1085, 1820, 3049, 5102, 8528, 14240, 23755, 39592, 65931, 109704, 182400, 303050, 503161, 834868, 1384397, 2294290, 3800080, 6290788, 10408679, 17213696, 28454415, 47014380, 77647104, 128186062

Offset

0,3

Comments

a(2*n) mod 2 = 0

a(4*n) mod 4 = 0

a(5*n) mod 5 = 0 and a(5*n+1) mod 5 = 0

a(n) = 2*A001629(n) - 3*A001629(n-1) [Johannes W. Meijer, Jun 27 2011]

Links

Table of n, a(n) for n=0..38.

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

Formula

a(n) = a(n-1) + a(n-2) + A000045(n-5), a(0) = a(1) = 0.

a(0)=0, a(1)=0, a(2)=2, a(3)=1, a(n)=2*a(n-1)+a(n-2)-2*a(n-3)-a(n-4). - Harvey P. Dale, Mar 16 2015

Maple

A191830:= proc(n) option remember: if n<=1 then 0 else procname(n-1)+procname(n-2)+A000045(n-5) fi: end proc: with(combinat): A000045:=fibonacci: seq(A191830(n), n=0..30); # Johannes W. Meijer, Jun 27 2011

Mathematica

CoefficientList[Series[x^2(2-3x)/(1-x-x^2)^2, {x, 0, 40}], x] (* or *) LinearRecurrence[{2, 1, -2, -1}, {0, 0, 2, 1}, 40] (* Harvey P. Dale, Mar 16 2015 *)

Prog

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -1, -2, 1, 2]^n*[0; 0; 2; 1])[1, 1] \\ Charles R Greathouse IV, Jul 06 2017

Crossrefs

Sequence in context: A021470 A138205 A137224 * A155944 A350087 A091232

Adjacent sequences: A191827 A191828 A191829 * A191831 A191832 A191833

Keyword

nonn,easy,less

Author

Paul Curtz, Jun 17 2011

Status

approved