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A076462 Sum of squares of numbers that can be written as t*n + u*(n+1) for nonnegative integers t,u in exactly three ways.

%I A076462 #18 Jul 05 2025 08:34:56
%S A076462 41,1471,12938,62870,218555,611821,1471316,3161388,6227565,11448635,
%T A076462 19895326,32995586,52606463,81092585,121411240,177204056,252895281,
%U A076462 353796663,486218930,657589870,876579011,1153228901,1499092988,1927380100,2453105525,3093248691
%N A076462 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 A076462 Fred. Schuh, Vragen betreffende een onbepaalde vergelijking, Nieuw Tijdschrift voor Wiskunde, 52 (1964-1965) 193-198.
%H A076462 Vincenzo Librandi, <a href="/A076462/b076462.txt">Table of n, a(n) for n = 1..1000</a>
%H A076462 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A076462 a(n) = n*(n+1)*(55*n^4+74*n^3+6*n^2-13*n+1)/6.
%F A076462 G.f.: x*(41+1184*x+3502*x^2+1760*x^3+113*x^4)/(1-x)^7.
%p A076462 seq(1/6*n*(n+1)*(55*n^4+74*n^3+6*n^2-13*n+1),n=1..30);
%t A076462 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 A076462 (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 A076462 Cf. A076389, A076460-A076465.
%K A076462 nonn,easy
%O A076462 1,1
%A A076462 _Floor van Lamoen_, Oct 13 2002