A110526 a(n+3) = 3*a(n+2) + 5*a(n+1) + a(n), a(0) = 0, a(1) = 1, a(2) = 3.
0, 1, 3, 14, 58, 247, 1045, 4428, 18756, 79453, 336567, 1425722, 6039454, 25583539, 108373609, 459077976, 1944685512, 8237820025, 34895965611, 147821682470, 626182695490, 2652552464431, 11236392553213, 47598122677284
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3, 5, 1).
Programs
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Maple
seriestolist(series(-x/((1+x)*(x^2+4*x-1)), x=0,25)); -or- Floretion Algebra Multiplication Program, FAMP Code: 1jbaseseq[(- 'i + 'j - i' + j' - 'kk' - 'ik' - 'jk' - 'ki' - 'kj')(+ .5'i + .5i' + .5'jj' + .5'kk')]
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Mathematica
Table[(Fibonacci[3n+1]-(-1)^n)/4, {n, 0, 20}] (* Vladimir Reshetnikov, Oct 28 2015 *) -
PARI
concat(0, Vec(x/((1+x)*(1-x^2-4*x)) + O(x^100))) \\ Altug Alkan, Oct 28 2015
Formula
G.f.: -x/((1+x)*(x^2+4*x-1)).
a(n) = (-1)^n/2 * Sum_{k=0..n} (-1)^k*Fibonacci(3*k). - Gary Detlefs, Jan 03 2013
a(n) = (Fibonacci(3*n+1)-(-1)^n)/4, where Fibonacci(n) = A000045(n). - Vladimir Reshetnikov, Oct 28 2015
Comments