A076463 Sum of squares of numbers that can be written as t*n + u*(n+1) for nonnegative integers t,u in exactly four ways.

85, 2803, 24026, 115270, 397655, 1107505, 2653588, 5685996, 11176665, 20511535, 35594350, 58962098, 93912091, 144640685, 216393640, 315628120, 450186333, 629480811, 864691330, 1168973470, 1557678815, 2048586793, 2662148156, 3421740100, 4353933025

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)*(97*n^4+146*n^3+30*n^2-19*n+1)/6.

G.f.: x*(85+2208*x+6190*x^2+2976*x^3+181*x^4)/(1-x)^7.

Maple

seq(1/6*n*(n+1)*(97*n^4+146*n^3+30*n^2-19*n+1), n=1..30);

Mathematica

CoefficientList[Series[(85 + 2208 x + 6190 x^2 + 2976 x^3 + 181 x^4)/(1 - x)^7, {x, 0, 50}], x] (* Vincenzo Librandi, Dec 30 2013 *)

Prog

(Magma) [n*(n+1)*(97*n^4+146*n^3+30*n^2-19*n+1)/6: n in [1..50]]; // Vincenzo Librandi, Dec 30 2013

Crossrefs

Cf. A076389, A076460-A076465.

Sequence in context: A262062 A220736 A157110 * A281162 A339198 A017801

Adjacent sequences: A076460 A076461 A076462 * A076464 A076465 A076466

Keyword

nonn,easy

Author

Floor van Lamoen, Oct 13 2002

Status

approved