cp's OEIS Frontend

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).

%I A352964 #14 Apr 13 2022 13:01:13
%S A352964 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,
%T A352964 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,
%U A352964 11,7,11,18,2,7,9,5,12,7,12,19,3,11,8,11,19
%N 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).
%C A352964 This sequence is a variant of the Fibonacci sequence (A000045) with variable steps.
%H A352964 Rémy Sigrist, <a href="/A352964/b352964.txt">Table of n, a(n) for n = 0..10945</a>
%H A352964 Rémy Sigrist, <a href="/A352964/a352964.png">Logarithmic scatterplot of the first F(27) = 196418 terms</a>
%F A352964 a(A000045(k)) = 1 for any k > 0.
%e A352964 a(0) = 0 by definition.
%e A352964 a(1) = 1 by definition.
%e A352964 a(2) = a(2-F(2)) + a(2-F(3)) = a(1) + a(0) = 1 + 0 = 1.
%e A352964 a(3) = a(3-F(3)) + a(3-F(4)) = a(1) + a(0) = 1 + 0 = 1.
%e A352964 a(4) = a(4-F(3)) + a(4-F(4)) = a(2) + a(1) = 1 + 1 = 2.
%e A352964 a(5) = a(5-F(4)) + a(5-F(5)) = a(2) + a(0) = 1 + 0 = 1.
%e A352964 a(6) = a(6-F(4)) + a(6-F(5)) = a(3) + a(1) = 1 + 1 = 2.
%e A352964 a(7) = a(7-F(4)) + a(7-F(5)) = a(4) + a(2) = 2 + 1 = 3.
%e A352964 a(8) = a(8-F(5)) + a(8-F(6)) = a(3) + a(0) = 1 + 0 = 1.
%o A352964 (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)]), ", ")) }
%Y A352964 See A352961 for a similar sequence.
%Y A352964 Cf. A000045, A005185, A072649.
%K A352964 nonn
%O A352964 0,5
%A A352964 _Rémy Sigrist_, Apr 11 2022