A076456 Sum of numbers that can be written as t*n + u*(n+1) for nonnegative integers t,u in exactly three ways.

9, 93, 390, 1110, 2535, 5019, 8988, 14940, 23445, 35145, 50754, 71058, 96915, 129255, 169080, 217464, 275553, 344565, 425790, 520590, 630399, 756723, 901140, 1065300, 1250925, 1459809, 1693818, 1954890, 2245035, 2566335, 2920944, 3311088, 3739065, 4207245

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)*(6*n^2+4*n-1)/2.

G.f.: 3*x*(3+16*x+5*x^2)/(1-x)^5.

Maple

seq(1/2*n*(n+1)*(6*n^2+4*n-1), n=1..40);

Mathematica

CoefficientList[Series[3 (3 + 16 x + 5 x^2)/(1 - x)^5, {x, 0, 50}], x] (* Vincenzo Librandi, Dec 30 2013 *)

Prog

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

Crossrefs

Cf. A002417, A076454-A076459.

Sequence in context: A015587 A024117 A261855 * A297580 A306475 A181958

Adjacent sequences: A076453 A076454 A076455 * A076457 A076458 A076459

Keyword

nonn,easy

Author

Floor van Lamoen, Oct 13 2002

Status

approved