A254362 a(n) = 3*2^n + 3^n + 6.
10, 15, 27, 57, 135, 345, 927, 2577, 7335, 21225, 62127, 183297, 543735, 1618905, 4832127, 14447217, 43243335, 129533385, 388206927, 1163834337, 3489930135, 10466644665, 31393642527, 94168344657, 282479868135, 847389272745, 2542067154927, 7626000138177
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Luciano Ancora, Demonstration of formulas, page 1.
- Luciano Ancora, Recurrence relations for partial sums of m-th powers
- Index entries for linear recurrences with constant coefficients, signature (6,-11,6).
Programs
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Mathematica
Table[3 * 2^n + 3^n + 6, {n, 0, 29}] (* Alonso del Arte, Jan 29 2015 *) LinearRecurrence[{6,-11,6},{10,15,27},30] (* Harvey P. Dale, Oct 11 2024 *) -
PARI
vector(30, n, n--; 3*2^n + 3^n + 6) \\ Colin Barker, Jan 30 2015
Formula
G.f.: -(47*x^2-45*x+10) / ((x-1)*(2*x-1)*(3*x-1)). - Colin Barker, Jan 30 2015
a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3). - Colin Barker, Jan 30 2015
Comments