A011369 a(n+1) = a(n) - F(n) if > 0, otherwise a(n) + F(n), where F() are Fibonacci numbers; a(0) = 0.
0, 0, 1, 2, 4, 1, 6, 14, 1, 22, 56, 1, 90, 234, 1, 378, 988, 1, 1598, 4182, 1, 6766, 17712, 1, 28658, 75026, 1, 121394, 317812, 1, 514230, 1346270, 1, 2178310, 5702888, 1, 9227466, 24157818, 1, 39088170, 102334156, 1, 165580142, 433494438, 1, 701408734, 1836311904
Offset: 0
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..4000
- Index entries for linear recurrences with constant coefficients, signature (1,0,4,-4,0,1,-1).
Programs
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Mathematica
Module[{n = 0, f}, NestList[If[(f = Fibonacci[n++]) < #, # - f, # + f] &, 0, 49]] (* Paolo Xausa, Nov 08 2024 *) Flatten[Join[{0, 0}, Table[{1, Fibonacci[{k, k+2}] + 1}, {k, 2, 49, 3}]]] (* Paolo Xausa, Nov 08 2024 *) LinearRecurrence[{1, 0, 4, -4, 0, 1, -1}, {0, 0, 1, 2, 4, 1, 6, 14, 1}, 50] (* Paolo Xausa, Nov 08 2024 *) -
PARI
a(n) = if (n==0, 0, my(d=a(n-1)-fibonacci(n-1)); if (d>0, d, d+2*fibonacci(n-1))) \\ Michel Marcus, Dec 29 2018
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PARI
a(n) = if (n<=1, 0, my(m=(n % 3)); if (m==0, fibonacci(n-1)+1, if (m==1, fibonacci(n)+1, 1))); \\ Michel Marcus, Dec 29 2018
Formula
a(n) = 0, if n <= 1; F(n-1)+1, if n == 0 (mod 3); F(n)+1, if n == 1 (mod 3); 1, if n == 2 (mod 3). - David W. Wilson; corrected by Michel Marcus, Dec 29 2018
For n>=1, a(n) = F(0)<+>F(1)<+>...<+>F(n-1), where operation <+> is defined in comment in A245618. - Vladimir Shevelev, Nov 05 2014
Empirical g.f.: -x^2*(2*x^6 - x^4 + 7*x^3 - 2*x^2 - x - 1) / ((x-1)*(x^2 + x - 1)*(x^4 - x^3 + 2*x^2 + x + 1)). - Colin Barker, Nov 06 2014
Extensions
Name edited by Michel Marcus, Dec 29 2018