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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 three ways.
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%I #16 Sep 08 2022 08:45:07

%S 41,1471,12938,62870,218555,611821,1471316,3161388,6227565,11448635,

%T 19895326,32995586,52606463,81092585,121411240,177204056,252895281,

%U 353796663,486218930,657589870,876579011,1153228901,1499092988,1927380100,2453105525,3093248691

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

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

%H Vincenzo Librandi, <a href="/A076462/b076462.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = n*(n+1)*(55*n^4+74*n^3+6*n^2-13*n+1)/6.

%F G.f.: x*(41+1184*x+3502*x^2+1760*x^3+113*x^4)/(1-x)^7.

%p seq(1/6*n*(n+1)*(55*n^4+74*n^3+6*n^2-13*n+1),n=1..30);

%t CoefficientList[Series[(41 + 1184 x + 3502 x^2 + 1760 x^3 + 113 x^4)/(1 - x)^7, {x, 0, 50}], x] (* _Vincenzo Librandi_, Dec 30 2013 *)

%o (Magma) [n*(n+1)*(55*n^4+74*n^3+6*n^2-13*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