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A272144 Convolution of A000217 and A001045. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A212587 A118425 A097809 * A036389 A036388 A037166

Adjacent sequences:  A272141 A272142 A272143 * A272145 A272146 A272147

KEYWORD

nonn,easy

AUTHOR

Patrick Okolo Edeogu, Apr 21 2016

STATUS

approved

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Last modified April 21 07:53 EDT 2019. Contains 322327 sequences. (Running on oeis4.)