A238604 a(n) = Sum_{k=0..3} f(n+k)^2 where f=A130519.

0, 1, 5, 14, 30, 65, 125, 216, 344, 533, 793, 1134, 1566, 2125, 2825, 3680, 4704, 5945, 7421, 9150, 11150, 13481, 16165, 19224, 22680, 26605, 31025, 35966, 41454, 47573, 54353, 61824, 70016, 79025, 88885, 99630, 111294, 123985, 137741, 152600, 168600, 185861

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..2500

Index entries for linear recurrences with constant coefficients, signature (3,-3,1,2,-6,6,-2,-1,3,-3,1).

Formula

G.f.: x * (1 + 2*x + 2*x^2 + 2*x^3 + 10*x^4 + 2*x^5 + 2*x^6 + 2*x^7 + x^8) / ( (1 - x)^3 * (1 - x^4)^2 ).

a(n) = a(-1 - n) for all n in Z. floor( sqrt( a(n))) = A054925(n+1).

Example

G.f. = x + 5*x^2 + 14*x^3 + 30*x^4 + 65*x^5 + 125*x^6 + 216*x^7 + ...

Mathematica

CoefficientList[Series[x*(1+2*x+2*x^2+2*x^3+10*x^4+2*x^5+2*x^6+2*x^7+ x^8)/((1-x)^3*(1-x^4)^2), {x, 0, 50}], x] (* G. C. Greubel, Aug 07 2018 *)

Prog

(PARI) {a(n) = if( n<0, n = -1-n); polcoeff( x * (1 + 2*x + 2*x^2 + 2*x^3 + 10*x^4 + 2*x^5 + 2*x^6 + 2*x^7 + x^8) / ( (1 - x)^3 * (1 - x^4)^2 ) + x * O(x^n), n)};
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1 +2*x+2*x^2+2*x^3+10*x^4+2*x^5+2*x^6+2*x^7+ x^8)/((1-x)^3*(1-x^4)^2))); // G. C. Greubel, Aug 07 2018

Crossrefs

Cf. A054925, A130519.

Sequence in context: A299899 A211804 A283591 * A166068 A070129 A359192

Adjacent sequences: A238601 A238602 A238603 * A238605 A238606 A238607

Keyword

nonn,easy

Author

Michael Somos, Mar 01 2014

Status

approved