A267799 a(n) = (1 + 2^n + 3^n)/2.
3, 7, 18, 49, 138, 397, 1158, 3409, 10098, 30037, 89598, 267769, 801258, 2399677, 7190838, 21556129, 64635618, 193841317, 581392878, 1743916489, 5231225178, 15692626957, 47075783718, 141223156849, 423661081938, 1270966468597, 3812865851358, 11438530445209, 34315457117898, 102946102918237
Offset: 1
Examples
a(3) = (1 + 2^3 + 3^3)/2 = 18.
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (6,-11,6).
Programs
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Mathematica
Table[(1 + 2^n + 3^n)/2, {n, 30}] (* Michael De Vlieger, Apr 07 2016 *) -
PARI
Vec(x*(3-11*x+9*x^2)/((1-x)*(1-2*x)*(1-3*x)) + O(x^50)) \\ Colin Barker, Apr 07 2016
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PARI
a(n) = (1 + 2^n + 3^n)/2 \\ Charles R Greathouse IV, Apr 07 2016
Formula
a(n) = (A007689(n)+1)/2.
From Colin Barker, Apr 07 2016: (Start)
a(n) = 6*a(n-1)-11*a(n-2)+6*a(n-3) for n>3.
G.f.: x*(3-11*x+9*x^2) / ((1-x)*(1-2*x)*(1-3*x)).
(End)
a(n) = A001550(n)/2, for n >= 1. - Altug Alkan, Apr 08 2016