A274972 Numbers x such that there exists n in N : (x+1)^3 - x^3 = 61*n^2.
4, 4387, 4273420, 4162307179, 4054082919412, 3948672601200595, 3846003059486460604, 3746003031267211428187, 3648603106451204444594020, 3553735679680441861823147779, 3461334903405643922211301343212, 3371336642181417499791945685141195
Offset: 1
Examples
4387 is in the sequence because ((4387+1)^3-4387^3)/61 = 946729 = 973^2.
Links
- Colin Barker, Table of n, a(n) for n = 1..300
- Index entries for linear recurrences with constant coefficients, signature (975,-975,1).
Programs
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PARI
Vec(x*(4+487*x-5*x^2)/((1-x)*(1-974*x+x^2)) + O(x^20))
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PARI
isok(x) = issquare(((x+1)^3-x^3)/61)
Formula
G.f.: x*(4+487*x-5*x^2) / ((1-x)*(1-974*x+x^2)).
a(n) = 975*a(n-1)-975*a(n-2)+a(n-3) for n>3.
a(n) = (-6-(27+2*sqrt(183))*(487+36*sqrt(183))^(-n)+(-27+2*sqrt(183))*(487+36*sqrt(183))^n)/12.