A076464 Sum of squares of numbers that can be written as t*n + u*(n+1) for nonnegative integers t,u in exactly five ways.

145, 4567, 38570, 183670, 630755, 1751365, 4187092, 8957100, 17583765, 32236435, 55893310, 92521442, 147274855, 226710785, 339024040, 494299480, 704782617, 985168335, 1352907730, 1828533070, 2436000875, 3203053117, 4161596540, 5348100100, 6804010525

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)*(151*n^4+242*n^3+66*n^2-25*n+1)/6.

G.f.: x*(145+3552*x+9646*x^2+4512*x^3+265*x^4)/(1-x)^7.

Maple

seq(1/6*n*(n+1)*(151*n^4+242*n^3+66*n^2-25*n+1), n=1..30);

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A076389, A076460-A076465.

Sequence in context: A232151 A264284 A008377 * A018232 A192842 A012813

Adjacent sequences: A076461 A076462 A076463 * A076465 A076466 A076467

Keyword

easy,nonn

Author

Floor van Lamoen, Oct 13 2002

Extensions

More terms from Vincenzo Librandi, Dec 30 2013

Status

approved