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%I #12 Sep 08 2022 08:45:07
%S 145,4567,38570,183670,630755,1751365,4187092,8957100,17583765,
%T 32236435,55893310,92521442,147274855,226710785,339024040,494299480,
%U 704782617,985168335,1352907730,1828533070,2436000875,3203053117,4161596540,5348100100,6804010525
%N Sum of squares of numbers that can be written as t*n + u*(n+1) for nonnegative integers t,u in exactly five ways.
%D Fred. Schuh, Vragen betreffende een onbepaalde vergelijking, Nieuw Tijdschrift voor Wiskunde, 52 (1964-1965) 193-198.
%H Vincenzo Librandi, <a href="/A076464/b076464.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = n*(n+1)*(151*n^4+242*n^3+66*n^2-25*n+1)/6.
%F G.f.: x*(145+3552*x+9646*x^2+4512*x^3+265*x^4)/(1-x)^7.
%p seq(1/6*n*(n+1)*(151*n^4+242*n^3+66*n^2-25*n+1),n=1..30);
%t CoefficientList[Series[(145 + 3552 x + 9646 x^2 + 4512 x^3 + 265 x^4)/(1 - x)^7, {x, 0, 50}], x] (* _Vincenzo Librandi_, Dec 30 2013 *)
%o (Magma) [n*(n+1)*(151*n^4+242*n^3+66*n^2-25*n+1)/6: n in [1..50]]; // _Vincenzo Librandi_, Dec 30 2013
%Y Cf. A076389, A076460-A076465.
%K easy,nonn
%O 1,1
%A _Floor van Lamoen_, Oct 13 2002
%E More terms from _Vincenzo Librandi_, Dec 30 2013
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