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.

41, 1471, 12938, 62870, 218555, 611821, 1471316, 3161388, 6227565, 11448635, 19895326, 32995586, 52606463, 81092585, 121411240, 177204056, 252895281, 353796663, 486218930, 657589870, 876579011, 1153228901, 1499092988, 1927380100, 2453105525, 3093248691

Offset

1,1

References

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Formula

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

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

Maple

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

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A076389, A076460-A076465.

Sequence in context: A094455 A239251 A197527 * A163050 A305863 A180667

Adjacent sequences: A076459 A076460 A076461 * A076463 A076464 A076465

Keyword

nonn,easy

Author

Floor van Lamoen, Oct 13 2002

Status

approved