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A076461 Sum of squares of numbers that can be written as t*n + u*(n+1) for nonnegative integers t,u in exactly two ways.

%I A076461 #17 Jul 05 2025 08:33:29
%S A076461 13,571,5306,26470,93455,264313,640276,1383276,2736465,5047735,
%T A076461 8796238,14621906,23357971,36066485,54076840,79027288,112909461,
%U A076461 158115891,217490530,294382270,392701463,516979441,672431036,865020100,1101528025,1389625263,1737945846,2156164906
%N A076461 Sum of squares of numbers that can be written as t*n + u*(n+1) for nonnegative integers t,u in exactly two ways.
%D A076461 Fred. Schuh, Vragen betreffende een onbepaalde vergelijking, Nieuw Tijdschrift voor Wiskunde, 52 (1964-1965) 193-198.
%H A076461 Vincenzo Librandi, <a href="/A076461/b076461.txt">Table of n, a(n) for n = 1..1000</a>
%H A076461 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A076461 a(n) = n*(n+1)*(25*n^4+26*n^3-6*n^2-7*n+1)/6.
%F A076461 G.f.: x*(13+480*x+1582*x^2+864*x^3+61*x^4)/(1-x)^7.
%p A076461 seq(1/6*n*(n+1)*(25*n^4+26*n^3-6*n^2-7*n+1),n=1..30);
%t A076461 CoefficientList[Series[(13 + 480 x + 1582 x^2 + 864 x^3 + 61 x^4)/(1 - x)^7, {x, 0, 50}], x] (* _Vincenzo Librandi_, Dec 30 2013 *)
%o A076461 (Magma) [n*(n+1)*(25*n^4+26*n^3-6*n^2-7*n+1)/6: n in [1..50]]; // _Vincenzo Librandi_, Dec 30 2013
%Y A076461 Cf. A076389, A076460-A076465.
%K A076461 easy,nonn
%O A076461 1,1
%A A076461 _Floor van Lamoen_, Oct 13 2002
%E A076461 More terms from _Vincenzo Librandi_, Dec 30 2013