A263946 Positive integers n such that (n+52)^3 - n^3 is a square.

26, 2626, 132522, 6624722, 331104826, 16548617826, 827099787722, 41338440769522, 2066094938689626, 103263408493713026, 5161104329746962922, 257951953078854434322, 12892436549612974754426, 644363875527569883288226, 32205301339828881189658122

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..588

Index entries for linear recurrences with constant coefficients, signature (51,-51,1).

Formula

a(n) = 51*a(n-1)-51*a(n-2)+a(n-3) for n>3.

G.f.: 26*x*(3*x^2-50*x-1) / ((x-1)*(x^2-50*x+1)).

a(n) = 26*(-6-(6+sqrt(39))*(25+4*sqrt(39))^(-n)+(-6+sqrt(39))*(25+4*sqrt(39))^n)/6. - Colin Barker, Mar 03 2016

Example

26 is in the sequence because (26+52)^3 - 26^3 = 676^2.

Mathematica

LinearRecurrence[{51, -51, 1}, {26, 2626, 132522}, 20] (* Harvey P. Dale, Feb 05 2019 *)

Prog

(PARI) Vec(26*x*(3*x^2-50*x-1)/((x-1)*(x^2-50*x+1)) + O(x^30))

Crossrefs

Cf. A263942 (4), A263943 (21), A263944 (28), A263945 (39), A263947 (57), A263948 (61), A263949 (84) where the parenthesized number is k in the expression (n+k)^3 - n^3.

Sequence in context: A087616 A177636 A232159 * A358164 A172010 A283571

Adjacent sequences: A263943 A263944 A263945 * A263947 A263948 A263949

Keyword

nonn,easy

Author

Colin Barker, Oct 30 2015

Status

approved