A076464 - OEIS

%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