A272144 Convolution of A000217 and A001045.

0, 0, 1, 4, 12, 30, 69, 150, 316, 652, 1329, 2688, 5412, 10866, 21781, 43618, 87300, 174672, 349425, 698940, 1397980, 2796070, 5592261, 11184654, 22369452, 44739060, 89478289, 178956760, 357913716, 715827642, 1431655509, 2863311258, 5726622772

Offset: 0

Author

Patrick Okolo Edeogu, Apr 21 2016

Keywords

• nonn
• easy

Examples

			a(4) = 12 = 0*10+1*6+1*3+3*1+5*0 from A000217: 0,1,3,6,10,... and A001045: 0,1,1,3,5,11,...
		

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-4,-2,5,-2).

Crossrefs

Partial Sums of A011377(n-2)=A178420(n-1).

Programs

Magma

m:=40; R:=PowerSeriesRing(Integers(), m); [0,0] cat Coefficients(R!(x^2/((1-x)^3*(1+x)*(1-2*x)))); // G. C. Greubel, Oct 26 2018

Maple

seq(coeff(series(x^2/((1-x)^3*(1+x)*(1-2*x)),x,n+1), x, n), n = 0 .. 35); # Muniru A Asiru, Oct 26 2018

Mathematica

CoefficientList[Series[x^2/((1 - x)^3 (1 + x) (1 - 2 x)), {x, 0, 30}], x] (* Michael De Vlieger, Apr 21 2016 *)

PARI

concat([0, 0], Vec(x^2/((1-x)^3*(1+x)*(1-2*x)) + O(x^40))) \\ Altug Alkan, Apr 21 2016

Formula

a(n) = Sum{k=0..n} A000217(k) * A001045(n-k). - Joerg Arndt, May 17 2016

a(n) = 4*a(n-1) - 4*a(n-2) - 2*a(n-3) + 5*a(n-4) - 2*a(n-5).

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

a(n+2) = (-105+(-1)^n+2^(7+n)-48*n-6*n^2)/24. - Colin Barker, Apr 21 2016

E.g.f.: (exp(-x) + 32*exp(2*x) - 3*(11 + 10*x + 2*x^2)*exp(x))/24. - Ilya Gutkovskiy, Apr 21 2016