A352961 a(0) = 0, a(1) = 1, and for any n > 1, a(n) = a(n-2^e) + a(n-2^(e+1)) with e as large as possible (e = A070939(n) - 2).

0, 1, 1, 2, 1, 3, 2, 5, 1, 4, 3, 7, 2, 7, 5, 12, 1, 5, 4, 9, 3, 10, 7, 17, 2, 9, 7, 16, 5, 17, 12, 29, 1, 6, 5, 11, 4, 13, 9, 22, 3, 13, 10, 23, 7, 24, 17, 41, 2, 11, 9, 20, 7, 23, 16, 39, 5, 22, 17, 39, 12, 41, 29, 70, 1, 7, 6, 13, 5, 16, 11, 27, 4, 17, 13

Offset: 0

Author

Rémy Sigrist, Apr 11 2022

Keywords

• nonn

Comments

This sequence is a variant of the Fibonacci sequence (A000045) with variable steps.

Examples

			a(0) = 0 by definition.
a(1) = 1 by definition.
a(2) = a(2-2^0) + a(2-2^1) = a(1) + a(0) = 1 + 0 = 1.
a(3) = a(3-2^0) + a(3-2^1) = a(2) + a(1) = 1 + 1 = 2.
a(4) = a(4-2^1) + a(4-2^2) = a(2) + a(0) = 1 + 0 = 1.
a(5) = a(5-2^1) + a(5-2^2) = a(3) + a(1) = 2 + 1 = 3.
a(6) = a(6-2^1) + a(6-2^2) = a(4) + a(2) = 1 + 1 = 2.
a(7) = a(7-2^1) + a(7-2^2) = a(5) + a(3) = 3 + 2 = 5.
a(8) = a(8-2^2) + a(8-2^3) = a(4) + a(0) = 1 + 0 = 1.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8191
• Rémy Sigrist, Logarithmic scatterplot of the first 2^17 terms

Crossrefs

See A352964 for a similar sequence.

Cf. A000045, A070939.

Programs

PARI

{ for (n=1, #a=vector(75), print1 (a[n]=if (n==1, 0, n==2, 1, e=#binary(n-1)-2; a[n-2^e]+a[n-2^(e+1)]),", ")) }

Formula

a(2*n) = a(n).