A127979 a(n) = (5*n/18 + 19/54)*2^n - (-1)^(n-1)*(3*n + 4)/27.
1, 4, 9, 24, 55, 130, 293, 660, 1459, 3206, 6977, 15096, 32463, 69482, 148061, 314332, 665067, 1402958, 2951545, 6194368, 12971271, 27107634, 56545429, 117751204, 244823075, 508287510, 1053857713, 2182280840, 4513692479, 9325646586
Offset: 1
Links
- G. C. Greubel, Table of n, a(n) for n = 1..1000
- W. Bosma, Signed bits and fast exponentiation, Journal de Théorie des Nombres de Bordeaux, Vol. 13, Fasc. 1 (2001), p. 37 (Proposition 5).
- Index entries for linear recurrences with constant coefficients, signature (2,3,-4,-4).
Programs
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Magma
[(5*n/18 +19/54)*2^n -(-1)^(n-1)*(3*n+4)/27: n in [1..50]]; // G. C. Greubel, May 08 2018
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Mathematica
Table[(5n/18 + 19/54)2^(n) - ((-1)^(n - 1) )(3n + 4)/27, {n, 1, 100}] LinearRecurrence[{2,3,-4,-4}, {1,4,9,24}, 50] (* G. C. Greubel, May 08 2018 *) -
PARI
for(n=1, 50, print1((5*n/18 +19/54)*2^n -(-1)^(n-1)*(3*n+4)/27, ", ")) \\ G. C. Greubel, May 08 2018
Formula
G.f.: x*(1+2*x-2*x^2-2*x^3)/((1+x)^2*(1-2x)^2). - Bruno Berselli, Apr 02 2012
a(n) = 2*a(n-1)+3*a(n-2)-4*a(n-3)-4*a(n-4). - Wesley Ivan Hurt, May 07 2021