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A129095
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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.
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5
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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
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OFFSET
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1,3
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COMMENTS
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Bisection A129096 is monotonically increasing.
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LINKS
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Paul D. Hanna, Table of n, a(n) for n = 1..1024
William J. Keith, Augustine O. Munagi, Binary compositions and semi-Pell compositions, arXiv:1912.11148 [math.CO], 2019.
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EXAMPLE
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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.
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MATHEMATICA
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Nest[Append[#1, If[EvenQ[#2], #1[[#2/2]], 2 #1[[-1]] + #1[[-2]] ] ] & @@ {#, Length@ # + 1} &, {1}, 61] (* Michael De Vlieger, Mar 10 2020 *)
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PROG
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(PARI) a(n)=if(n==1 || n==0, 1, if(n%2==0, a(n/2), 2*a(n-1)+a(n-2)))
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CROSSREFS
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Cf. A129096, A129097, A129098, A129099; A030067 (semi-Fibonacci).
Sequence in context: A212641 A195835 A077881 * A105604 A117576 A112447
Adjacent sequences: A129092 A129093 A129094 * A129096 A129097 A129098
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KEYWORD
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easy,nonn
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AUTHOR
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Paul D. Hanna, Apr 11 2007
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STATUS
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approved
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