(MAGMAMagma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1+x+2*x^2+7*x^3+2*x^4+x^5+x^6)/((1-x)*(1-x^4)^2))); // G. C. Greubel, Aug 10 2018
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Select[(Range[0, 500]^2-49)/120, IntegerQ] (* or *) LinearRecurrence[ {1, 0, 0, 2, -2, 0, 0, -1, 1}, {0, 1, 2, 4, 11, 15, 18, 23, 37}, 80] (* Harvey P. Dale, Oct 23 2019 *)
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G. C. Greubel, <a href="/A214429/b214429_1.txt">Table of n, a(n) for n = 0..5000</a>
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G. C. Greubel, <a href="/A214429/b214429_1.txt">Table of n, a(n) for n = 0..49995000</a>
G. C. Greubel, <a href="/A214429/b214429.txt">Table of n, a(n) for n = 0..4999</a>
G.f.: x * (1 + x + 2*x^2 + 7*x^3 + 2*x^4 + x^5 + x^76) / ((1 - x) * (1 - x^4)^2).
CoefficientList[Series[x*(1+x+2*x^2+7*x^3+2*x^4+x^5+x^6)/((1-x)*(1- x^4)^2), {x, 0, 50}], x] (* G. C. Greubel, Aug 10 2018 *)
(MAGMA) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1+x+2*x^2+7*x^3+2*x^4+x^5+x^6)/((1-x)*(1-x^4)^2))); // G. C. Greubel, Aug 10 2018
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<a href="/index/Rec#order_09">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (1,0,0,2,-2,0,0,-1,1).
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