cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A083327 a(n) = (5^n - 4^n + 3^n - 2^n)/2.

Original entry on oeis.org

0, 1, 7, 40, 217, 1156, 6097, 31900, 165697, 855076, 4387537, 22404460, 113945377, 577590196, 2919923377, 14729076220, 74167952257, 372944296516, 1873182473617, 9399885079180, 47135702874337, 236224784974036
Offset: 0

Views

Author

Paul Barry, Apr 27 2003

Keywords

Comments

Binomial transform of A053154 (with leading zero).

Crossrefs

Cf. A083328.

Programs

  • Mathematica
    Table[(5^n-4^n+3^n-2^n)/2,{n,0,30}] (* or *) LinearRecurrence[{14,-71,154,-120},{0,1,7,40},30] (* Harvey P. Dale, Apr 04 2013 *)

Formula

G.f.: x(1-7x+13x^2)/((1-2x)(1-3x)(1-4x)(1-5x)).
E.g.f.: exp(5x) - exp(4x) + exp(3x) - exp(2x).
a(n) = 14*a(n-1) - 71*a(n-2) + 154*a(n-3) - 120*a(n-4), n > 3. - Harvey P. Dale, Apr 04 2013