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.

13, 571, 5306, 26470, 93455, 264313, 640276, 1383276, 2736465, 5047735, 8796238, 14621906, 23357971, 36066485, 54076840, 79027288, 112909461, 158115891, 217490530, 294382270, 392701463, 516979441, 672431036, 865020100, 1101528025, 1389625263, 1737945846, 2156164906

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)*(25*n^4+26*n^3-6*n^2-7*n+1)/6.

G.f.: x*(13+480*x+1582*x^2+864*x^3+61*x^4)/(1-x)^7.

Maple

seq(1/6*n*(n+1)*(25*n^4+26*n^3-6*n^2-7*n+1), n=1..30);

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A076389, A076460-A076465.

Sequence in context: A265503 A050286 A096761 * A168601 A142210 A109875

Adjacent sequences: A076458 A076459 A076460 * A076462 A076463 A076464

Keyword

easy,nonn

Author

Floor van Lamoen, Oct 13 2002

Extensions

More terms from Vincenzo Librandi, Dec 30 2013

Status

approved