A076459 Sum of numbers that can be written as t*n + u*(n+1) for nonnegative integers t,u in exactly n ways.

1, 57, 390, 1510, 4335, 10311, 21532, 40860, 72045, 119845, 190146, 290082, 428155, 614355, 860280, 1179256, 1586457, 2099025, 2736190, 3519390, 4472391, 5621407, 6995220, 8625300, 10545925, 12794301, 15410682, 18438490, 21924435, 25918635, 30474736, 35650032

Offset: 1

Author

Floor van Lamoen, Oct 13 2002

Keywords

• easy
• nonn

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 (6,-15,20,-15,6,-1).

Crossrefs

Cf. A002417, A076454-A076458.

Programs

Magma

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

Maple

seq(1/2*n*(n+1)*(2*n^3+2*n^2-2*n-1),n=1..35);

Mathematica

CoefficientList[Series[(1 + 51 x + 63 x^2 + 5 x^3)/(1 - x)^6, {x, 0, 50}], x] (* Vincenzo Librandi, Dec 30 2013 *)

Formula

a(n) = n*(n+1)*(2*n^3+2*n^2-2*n-1)/2.

G.f.: x*(1+51*x+63*x^2+5*x^3)/(1-x)^6.

Extensions

More terms from Vincenzo Librandi, Dec 30 2013