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

%I #16 Sep 08 2022 08:45:07

%S 85,2803,24026,115270,397655,1107505,2653588,5685996,11176665,

%T 20511535,35594350,58962098,93912091,144640685,216393640,315628120,

%U 450186333,629480811,864691330,1168973470,1557678815,2048586793,2662148156,3421740100,4353933025

%N 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 Fred. Schuh, Vragen betreffende een onbepaalde vergelijking, Nieuw Tijdschrift voor Wiskunde, 52 (1964-1965) 193-198.

%H Vincenzo Librandi, <a href="/A076463/b076463.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = n*(n+1)*(97*n^4+146*n^3+30*n^2-19*n+1)/6.

%F G.f.: x*(85+2208*x+6190*x^2+2976*x^3+181*x^4)/(1-x)^7.

%p seq(1/6*n*(n+1)*(97*n^4+146*n^3+30*n^2-19*n+1),n=1..30);

%t 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 (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 Cf. A076389, A076460-A076465.

%K nonn,easy

%O 1,1

%A _Floor van Lamoen_, Oct 13 2002