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

0,4

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).

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

Example

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,...

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 *)

Prog

(PARI) concat([0, 0], Vec(x^2/((1-x)^3*(1+x)*(1-2*x)) + O(x^40))) \\ Altug Alkan, Apr 21 2016
(Magma) m:=40; R<x>:=PowerSeriesRing(Integers(), m); [0, 0] cat Coefficients(R!(x^2/((1-x)^3*(1+x)*(1-2*x)))); // G. C. Greubel, Oct 26 2018

Crossrefs

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

Sequence in context: A338223 A118425 A097809 * A036389 A037166 A118892

Adjacent sequences: A272141 A272142 A272143 * A272145 A272146 A272147

Keyword

nonn,easy

Author

Patrick Okolo Edeogu, Apr 21 2016

Status

approved