A174676 Sequence built as it follows in comments.

5, 16, 2, 48, 2, 6, 145, 2, 6, 19, 2, 435, 2, 6, 19, 2, 57, 2, 6, 1306, 2, 6, 19, 2, 57, 2, 6, 172, 2, 6

Offset

0,1

Comments

With the Fibonacci sequence A000045 without 0 i.e. here F(0)=F(1)=1, F(2)=2, F(3)=3, ..., this sequence satisfies: a(F(2*n)-2)=(43*9^(n-1)-3)/8; a(F(2*n+1)-2)=(129*9^(n-1)-1)/8; a(F(2*n)+F(2*n-2)-2)=(51*9^(n-2)-3)/8; a(F(2*n+1)+F(2*n-1)-2)=(17*9^(n-1)-1)/8; and the recurrence rules: with A the finite sequence between a(F(2*n-2)-2) and a(F(2*n-1)-2), and B the finite sequence between a(F(2*n-1)-2) and a(F(2*n)-2), the next step of the sequence between a(F(2*n)-2) and a(F(2*n+1)-2) is given by: "B - a(F(2*n)+F(2*n-2)-2) - A". In the same vein, with A' the finite sequence between a(F(2*n-1)-2) and a(F(2*n)-2) and B' the finite sequence between a(F(2*n)-2) and a(F(2*n+1)-2), the next step of the sequence between a(F(2*n+1)-2) and a(F(2*n+2)-2) is given by: "B' - a(F(2*n+1)+F(2*n-1)-2) - A'". It seems that this sequence gives the numbers of 2 in the successive sets of 2 in the sequence A174664.

Links

Table of n, a(n) for n=0..29.

Example

a(F(4)-2)=a(3)=(9*43-3)/8=48. a(F(5)-2)=a(6)= (129*9-1)/8=145. a(F(6)-2)=a(11)=(43*9^2-3)/8=435. Between a(F(5)-2)=a(7)=145 and a(F(6)-2)=a(11)=435, there is: "2, 6, 19, 2". Between a(F(6)-2)=435 and a(F(7)-2)=a(19)=1306 there is "2, 6, 19, 2, 57, 2, 6". Then between a(19)=1306 and a(F(8)-2)=a(32)=3918, there is "2, 6, 19, 2, 57, 2, 6, a(F(7)+F(5)-2)=a(27)=172, 2, 6, 19, 2".

Crossrefs

Cf. A174664, A174665, A174353.

Sequence in context: A138489 A022509 A138074 * A302062 A161846 A069937

Adjacent sequences: A174673 A174674 A174675 * A174677 A174678 A174679

Keyword

easy,nonn

Author

Richard Choulet, Mar 26 2010

Status

approved