A097857 a(0) = 1, a(1) = 1, a(n) = floor((a(n-1)+a(n-2))/2) + 3 if a(n-2) is even, a(n) = floor((a(n-1)-a(n-2))/2) + 3 if a(n-2) is odd.

1, 1, 3, 4, 3, 6, 4, 8, 9, 11, 4, -1, 4, 5, 7, 4, 1, 5, 5, 3, 2, 2, 5, 6, 3, 7, 5, 2, 1, 4, 4, 7, 8, 3, 8, 5, 9, 5, 1, 1, 3, 4, 3, 6, 4, 8, 9, 11, 4, -1, 4, 5, 7, 4, 1, 5, 5, 3, 2, 2, 5, 6, 3, 7, 5, 2, 1, 4, 4, 7, 8, 3, 8, 5, 9, 5, 1, 1, 3, 4, 3, 6, 4, 8, 9, 11, 4, -1, 4, 5, 7, 4, 1, 5, 5, 3, 2, 2, 5, 6, 3, 7, 5, 2, 1, 4, 4, 7, 8, 3, 8, 5, 9, 5

Offset

0,3

Comments

The series is periodic with period 38.

Links

Table of n, a(n) for n=0..113.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Mathematica

nxt[{a_, b_}]:={b, If[EvenQ[a], Floor[(a+b)/2]+3, Floor[(b-a)/2]+3]}; NestList[nxt, {1, 1}, 120][[All, 1]] (* Harvey P. Dale, Mar 08 2022 *)

Crossrefs

Sequence in context: A061112 A078809 A245218 * A176058 A110738 A175028

Adjacent sequences: A097854 A097855 A097856 * A097858 A097859 A097860

Keyword

sign,easy

Author

Gerald McGarvey, Aug 31 2004

Extensions

More terms from Emeric Deutsch, Nov 17 2004

Status

approved