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
Links
- Index entries for linear recurrences with constant coefficients, signature (14,-71,154,-120).
Crossrefs
Cf. A083328.
Programs
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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
Comments