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A129095 Semi-Pell numbers: a(n) = a(n/2) (n even), a(n) = 2*a(n-1) + a(n-2) (n odd >1), with a(1) = 1. 5
1, 1, 3, 1, 5, 3, 11, 1, 13, 5, 23, 3, 29, 11, 51, 1, 53, 13, 79, 5, 89, 23, 135, 3, 141, 29, 199, 11, 221, 51, 323, 1, 325, 53, 431, 13, 457, 79, 615, 5, 625, 89, 803, 23, 849, 135, 1119, 3, 1125, 141, 1407, 29, 1465, 199, 1863, 11, 1885, 221, 2327, 51, 2429, 323 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Bisection A129096 is monotonically increasing.
LINKS
Cristina Ballantine and George Beck, Partitions enumerated by self-similar sequences, arXiv:2303.11493 [math.CO], 2023.
William J. Keith and Augustine O. Munagi, Binary compositions and semi-Pell compositions, arXiv:1912.11148 [math.CO], 2019.
EXAMPLE
Terms may be arranged into an irregular-shaped triangle:
1;
1, 3;
1, 5, 3, 11;
1, 13, 5, 23, 3, 29, 11, 51;
1, 53, 13, 79, 5, 89, 23, 135, 3, 141, 29, 199, 11, 221, 51, 323;
...
where final terms of rows form A129097,
central terms are given by A129098,
and row sums are equal to A129099.
MATHEMATICA
Nest[Append[#1, If[EvenQ[#2], #1[[#2/2]], 2 #1[[-1]] + #1[[-2]] ] ] & @@ {#, Length@ # + 1} &, {1}, 61] (* Michael De Vlieger, Mar 10 2020 *)
PROG
(PARI) a(n)=if(n==1 || n==0, 1, if(n%2==0, a(n/2), 2*a(n-1)+a(n-2)))
CROSSREFS
Cf. A030067 (semi-Fibonacci), A074364 (semi-tribonacci).
Sequence in context: A212641 A195835 A077881 * A105604 A117576 A112447
KEYWORD
easy,nonn
AUTHOR
Paul D. Hanna, Apr 11 2007
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)