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

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..300

Index entries for linear recurrences with constant coefficients, signature (975,-975,1).

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.

Example

4387 is in the sequence because ((4387+1)^3-4387^3)/61 = 946729 = 973^2.

Prog

(PARI) Vec(x*(4+487*x-5*x^2)/((1-x)*(1-974*x+x^2)) + O(x^20))
(PARI) isok(x) = issquare(((x+1)^3-x^3)/61)

Crossrefs

Cf. A145336, A145212, A274971, A275060.

Sequence in context: A249804 A079682 A127235 * A344670 A344671 A203036

Adjacent sequences: A274969 A274970 A274971 * A274973 A274974 A274975

Keyword

nonn,easy

Author

Colin Barker, Jul 13 2016

Status

approved