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A272569
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A variation on Stern's diatomic sequence.
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1
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0, 0, 1, 0, 2, 1, 2, 0, 3, 2, 6, 1, 6, 2, 3, 0, 4, 3, 10, 2, 15, 6, 12, 1, 12, 6, 15, 2, 10, 3, 4, 0, 5, 4, 14, 3, 24, 10, 21, 2, 28, 15, 40, 6, 35, 12, 20, 1, 20, 12, 35, 6, 40, 15, 28, 2, 21, 10, 24, 3, 14, 4, 5, 0, 6, 5, 18, 4, 33, 14, 30, 3, 44, 24, 65, 10
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OFFSET
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1,5
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COMMENTS
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LINKS
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Sam Northshield, Three analogues of Stern's diatomic sequence, arXiv preprint arXiv:1503.03433 [math.CO], 2015; also, Proceedings of the 16th International Conference on Fibonacci Numbers and Their Applications, Rochester Institute of Technology, Rochester, New York, July 20-27, 2014.
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FORMULA
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a(2n) = a(n), a(2n+1) = a(n) + a(n+1) + (4a(n)*a(n+1)+1)^(1/2).
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MATHEMATICA
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nn = 100;
a[_] = 0; a[1] = 0; Do[a[n] = If[EvenQ[n], a[n/2], m = (n-1)/2; a[m] + a[m + 1] + Sqrt[1 + 4 a[m] a[m+1]] // Floor], {n, 2, nn}];
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PROG
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(PARI) lista(nn) = {va = vector(nn); va[1] = 0; for (n=2, nn, if (n % 2 == 0, va[n] = va[n/2], m = (n-1)/2; va[n] = va[m] + va[m+1] + sqrtint(1 + 4*va[m]*va[m+1])); ); va; } \\ Michel Marcus, May 03 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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