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A263948
Positive integers n such that (n+61)^3 - n^3 is a square.
8
244, 267607, 260678620, 253900737919, 247299058084132, 240869028673236295, 234606186628674096844, 228506184907299897119407, 222564789493523471120235220, 216777876460506953571212014519, 211141429107744279254889381935932, 205651535173066467487308686793612895
OFFSET
1,1
FORMULA
a(n) = 975*a(n-1)-975*a(n-2)+a(n-3) for n>3.
G.f.: 61*x*(5*x^2-487*x-4) / ((x-1)*(x^2-974*x+1)).
EXAMPLE
244 is in the sequence because (244+61)^3 - 244^3 = 3721^2.
MATHEMATICA
LinearRecurrence[{975, -975, 1}, {244, 267607, 260678620}, 15] (* Paolo Xausa, Mar 05 2024 *)
PROG
(PARI) Vec(61*x*(5*x^2-487*x-4)/((x-1)*(x^2-974*x+1)) + O(x^15))
CROSSREFS
Cf. A263942 (4), A263943 (21), A263944 (28), A263945 (39), A263946 (52), A263947 (57), A263949 (84) where the parenthesized number is k in the expression (n+k)^3 - n^3.
Sequence in context: A218246 A217471 A146552 * A306981 A164656 A291587
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Oct 30 2015
STATUS
approved