A076389 Sum of squares of numbers that cannot be written as t*n + u*(n+1) for nonnegative integers t,u.

0, 1, 30, 220, 950, 3045, 8036, 18480, 38340, 73425, 131890, 224796, 366730, 576485, 877800, 1300160, 1879656, 2659905, 3693030, 5040700, 6775230, 8980741, 11754380, 15207600, 19467500, 24678225, 31002426, 38622780, 47743570, 58592325, 71421520, 86510336, 104166480

Offset

1,3

References

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

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

a(n) = n^2*(n^2-1)*(n^2-n-1)/12.

G.f.: (1+23*x+31*x^2+5*x^3)*x^2/(1-x)^7.

E.g.f.: exp(x)*x^2*(6 + 54*x + 53*x^2 + 14*x^3 + x^4)/12. - Stefano Spezia, May 18 2026

Maple

seq(n^2*(n^2-1)*(n^2-n-1)/12, n=1..40);

Mathematica

A076389[n_] := n^2*(n^2 - 1)*(n^2 - n - 1)/12; Array[A076389, 50] (* Paolo Xausa, May 17 2026 *)

Crossrefs

Cf. A002417, A076460-A076465.

Sequence in context: A042754 A215192 A244836 * A342896 A189410 A210101

Adjacent sequences: A076386 A076387 A076388 * A076390 A076391 A076392

Keyword

easy,nonn

Author

Floor van Lamoen, Oct 09 2002

Extensions

More terms from Paolo Xausa, May 17 2026

Status

approved