cp's OEIS Frontend

A076463 Sum of squares of numbers that can be written as t*n + u*(n+1) for nonnegative integers t,u in exactly four ways.

%I A076463 #18 Jul 05 2025 08:36:01
%S A076463 85,2803,24026,115270,397655,1107505,2653588,5685996,11176665,
%T A076463 20511535,35594350,58962098,93912091,144640685,216393640,315628120,
%U A076463 450186333,629480811,864691330,1168973470,1557678815,2048586793,2662148156,3421740100,4353933025
%N A076463 Sum of squares of numbers that can be written as t*n + u*(n+1) for nonnegative integers t,u in exactly four ways.
%D A076463 Fred. Schuh, Vragen betreffende een onbepaalde vergelijking, Nieuw Tijdschrift voor Wiskunde, 52 (1964-1965) 193-198.
%H A076463 Vincenzo Librandi, <a href="/A076463/b076463.txt">Table of n, a(n) for n = 1..1000</a>
%H A076463 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A076463 a(n) = n*(n+1)*(97*n^4+146*n^3+30*n^2-19*n+1)/6.
%F A076463 G.f.: x*(85+2208*x+6190*x^2+2976*x^3+181*x^4)/(1-x)^7.
%p A076463 seq(1/6*n*(n+1)*(97*n^4+146*n^3+30*n^2-19*n+1),n=1..30);
%t A076463 CoefficientList[Series[(85 + 2208 x + 6190 x^2 + 2976 x^3 + 181 x^4)/(1 - x)^7, {x, 0, 50}], x] (* _Vincenzo Librandi_, Dec 30 2013 *)
%o A076463 (Magma) [n*(n+1)*(97*n^4+146*n^3+30*n^2-19*n+1)/6: n in [1..50]]; // _Vincenzo Librandi_, Dec 30 2013
%Y A076463 Cf. A076389, A076460-A076465.
%K A076463 nonn,easy
%O A076463 1,1
%A A076463 _Floor van Lamoen_, Oct 13 2002