A352964 a(0) = 0, a(1) = 1, and for any n > 1, a(n) = a(n-F(e)) + a(n-F(e+1)) with e as large as possible (where F(k) is the k-th Fibonacci number).
0, 1, 1, 1, 2, 1, 2, 3, 1, 3, 2, 3, 5, 1, 3, 4, 2, 5, 3, 5, 8, 1, 4, 3, 4, 7, 2, 5, 7, 3, 8, 5, 8, 13, 1, 4, 5, 3, 7, 4, 7, 11, 2, 7, 5, 7, 12, 3, 8, 11, 5, 13, 8, 13, 21, 1, 5, 4, 5, 9, 3, 7, 10, 4, 11, 7, 11, 18, 2, 7, 9, 5, 12, 7, 12, 19, 3, 11, 8, 11, 19
Offset: 0
Keywords
Examples
a(0) = 0 by definition. a(1) = 1 by definition. a(2) = a(2-F(2)) + a(2-F(3)) = a(1) + a(0) = 1 + 0 = 1. a(3) = a(3-F(3)) + a(3-F(4)) = a(1) + a(0) = 1 + 0 = 1. a(4) = a(4-F(3)) + a(4-F(4)) = a(2) + a(1) = 1 + 1 = 2. a(5) = a(5-F(4)) + a(5-F(5)) = a(2) + a(0) = 1 + 0 = 1. a(6) = a(6-F(4)) + a(6-F(5)) = a(3) + a(1) = 1 + 1 = 2. a(7) = a(7-F(4)) + a(7-F(5)) = a(4) + a(2) = 2 + 1 = 3. a(8) = a(8-F(5)) + a(8-F(6)) = a(3) + a(0) = 1 + 0 = 1.
Links
- Rémy Sigrist, Table of n, a(n) for n = 0..10945
- Rémy Sigrist, Logarithmic scatterplot of the first F(27) = 196418 terms
Programs
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PARI
{ e=2; for (n=1, #a=vector(81), print1 (a[n]=if (n==1, 0, n==2, 1, if (n>fibonacci(e+2), e++); a[n-fibonacci(e)]+a[n-fibonacci(e+1)]), ", ")) }
Formula
a(A000045(k)) = 1 for any k > 0.
Comments