A074742 a(n) = (n^3 + 6n^2 - n + 12)/6.

2, 3, 7, 15, 28, 47, 73, 107, 150, 203, 267, 343, 432, 535, 653, 787, 938, 1107, 1295, 1503, 1732, 1983, 2257, 2555, 2878, 3227, 3603, 4007, 4440, 4903, 5397, 5923, 6482, 7075, 7703, 8367, 9068, 9807, 10585, 11403, 12262, 13163, 14107, 15095, 16128, 17207, 18333

Offset: 0

Author

Susanna Cuyler, Sep 06 2002

Keywords

• nonn
• easy

References

• A. Schultze, Advanced Algebra, Macmillan, London, 1910; p. 552.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A027965.

Programs

Magma

[(n^3 + 6*n^2 - n + 12)/6: n in [0..50]]; // Vincenzo Librandi, Jan 13 2012

Mathematica

Table[(n^3 + 6n^2 - n + 12)/6, {n, 0, 49}] (* Alonso del Arte, Jan 13 2012 *)
CoefficientList[Series[(2-5x+7x^2-3x^3)/(1-x)^4,{x,0,50}],x] (* or *) LinearRecurrence[ {4,-6,4,-1},{2,3,7,15},50] (* Harvey P. Dale, Aug 05 2022 *)

PARI

a(n)=n*(n^2+6*n-1)/6+2 \\ Charles R Greathouse IV, Jan 13 2012

Formula

From R. J. Mathar, Sep 23 2008: (Start)

G.f.: (2 - 5*x + 7*x^2 - 3*x^3)/(1-x)^4.

a(n) = A027965(n+1), n > 0. (End)

E.g.f.: exp(x)*(12 + 6*x + 9*x^2 + x^3)/6. - Stefano Spezia, Jul 12 2023