A263948 - OEIS

%I #9 Mar 05 2024 05:05:44

%S 244,267607,260678620,253900737919,247299058084132,240869028673236295,

%T 234606186628674096844,228506184907299897119407,

%U 222564789493523471120235220,216777876460506953571212014519,211141429107744279254889381935932,205651535173066467487308686793612895

%N Positive integers n such that (n+61)^3 - n^3 is a square.

%H Colin Barker, <a href="/A263948/b263948.txt">Table of n, a(n) for n = 1..334</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (975,-975,1).

%F a(n) = 975*a(n-1)-975*a(n-2)+a(n-3) for n>3.

%F G.f.: 61*x*(5*x^2-487*x-4) / ((x-1)*(x^2-974*x+1)).

%e 244 is in the sequence because (244+61)^3 - 244^3 = 3721^2.

%t LinearRecurrence[{975, -975, 1}, {244, 267607, 260678620}, 15] (* _Paolo Xausa_, Mar 05 2024 *)

%o (PARI) Vec(61*x*(5*x^2-487*x-4)/((x-1)*(x^2-974*x+1)) + O(x^15))

%Y 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.

%K nonn,easy

%O 1,1

%A _Colin Barker_, Oct 30 2015