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

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

Offset

0,3

Comments

Binomial transform of A053154 (with leading zero).

Links

Table of n, a(n) for n=0..21.

Index entries for linear recurrences with constant coefficients, signature (14,-71,154,-120).

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

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 *)

Crossrefs

Cf. A083328.

Sequence in context: A081039 A227748 A349594 * A026716 A026782 A099459

Adjacent sequences: A083324 A083325 A083326 * A083328 A083329 A083330

Keyword

easy,nonn

Author

Paul Barry, Apr 27 2003

Status

approved