A129096 A bisection of A129095: a(n) = A129095(2n-1) for n>=1.

1, 3, 5, 11, 13, 23, 29, 51, 53, 79, 89, 135, 141, 199, 221, 323, 325, 431, 457, 615, 625, 803, 849, 1119, 1125, 1407, 1465, 1863, 1885, 2327, 2429, 3075, 3077, 3727, 3833, 4695, 4721, 5635, 5793, 7023, 7033, 8283, 8461, 10067, 10113, 11811, 12081, 14319

Offset: 1

Author

Paul D. Hanna, Apr 11 2007

Keywords

• easy
• nonn

Comments

b(n)=A129095(n) obeys the recurrence: b(n) = b(n/2) (n even), b(n) = 2*b(n-1) + b(n-2) (n odd >1), with b(1) = 1.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• William J. Keith and Augustine O. Munagi, Binary compositions and semi-Pell compositions, arXiv:1912.11148 [math.CO], 2019.
• William J. Keith and Augustine O. Munagi, Power compositions and semi-Pell compositions, Univ. Rochester, Online J. Analytic Comb. (2023) Issue 18, Art No. 2. See p. 2.

Crossrefs

Cf. A129095, A129097, A129098, A129099.

Programs

Mathematica

With[{s = Nest[Append[#1, If[EvenQ[#2], #1[[#2/2]], 2 #1[[-1]] + #1[[-2]] ] ] & @@ {#, Length@ # + 1} &, {1}, 192]}, Table[s[[i]], {i, 1, Floor[Length[s]/2], 2}]] (* Michael De Vlieger, Mar 10 2020 *)