A129959 A129957(n) - n*(n-1)/2.

1, 1, 8, 24, 59, 115, 202, 322, 485, 693, 956, 1276, 1663, 2119, 2654, 3270, 3977, 4777, 5680, 6688, 7811, 9051, 10418, 11914, 13549, 15325, 17252, 19332, 21575, 23983, 26566, 29326, 32273, 35409, 38744, 42280, 46027, 49987, 54170, 58578, 63221

Offset

0,3

Links

Table of n, a(n) for n=0..40.

Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).

Formula

a(n) = (1+(-1)^n+n-n^2+2*n^3)/2. G.f.: (1-2*x+7*x^2+4*x^3+2*x^4)/((1-x)^4*(1+x)). [Colin Barker, Sep 10 2012]

Mathematica

f[n_]:= If[Mod[n, 2] == 0, n^3 + 1, n^3]; Table[f[n] - n*(n - 1)/2, {n, 0, 40}]

Crossrefs

Cf. A129957, A129958.

Sequence in context: A302489 A099041 A306056 * A256533 A177719 A317234

Adjacent sequences: A129956 A129957 A129958 * A129960 A129961 A129962

Keyword

nonn,easy

Author

Roger L. Bagula, Jun 10 2007

Extensions

Edited, corrected and extended by Stefan Steinerberger, Jul 21 2007

Status

approved