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%I #12 Sep 08 2022 08:46:07
%S 0,1,5,14,30,65,125,216,344,533,793,1134,1566,2125,2825,3680,4704,
%T 5945,7421,9150,11150,13481,16165,19224,22680,26605,31025,35966,41454,
%U 47573,54353,61824,70016,79025,88885,99630,111294,123985,137741,152600,168600,185861
%N a(n) = Sum_{k=0..3} f(n+k)^2 where f=A130519.
%H G. C. Greubel, <a href="/A238604/b238604.txt">Table of n, a(n) for n = 0..2500</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,2,-6,6,-2,-1,3,-3,1).
%F 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 ).
%F a(n) = a(-1 - n) for all n in Z. floor( sqrt( a(n))) = A054925(n+1).
%e G.f. = x + 5*x^2 + 14*x^3 + 30*x^4 + 65*x^5 + 125*x^6 + 216*x^7 + ...
%t 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 *)
%o (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)};
%o (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
%Y Cf. A054925, A130519.
%K nonn,easy
%O 0,3
%A _Michael Somos_, Mar 01 2014
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