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

Author

Floor van Lamoen, Oct 13 2002

Keywords

• nonn
• easy

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
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A002417, A076454-A076459.

Programs

Magma

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

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 *)

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.