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A317316
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Multiples of 16 and odd numbers interleaved.
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4
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0, 1, 16, 3, 32, 5, 48, 7, 64, 9, 80, 11, 96, 13, 112, 15, 128, 17, 144, 19, 160, 21, 176, 23, 192, 25, 208, 27, 224, 29, 240, 31, 256, 33, 272, 35, 288, 37, 304, 39, 320, 41, 336, 43, 352, 45, 368, 47, 384, 49, 400, 51, 416, 53, 432, 55, 448, 57, 464, 59, 480, 61, 496, 63, 512, 65, 528, 67, 544, 69
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OFFSET
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0,3
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COMMENTS
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Partial sums give the generalized 20-gonal numbers (A218864).
a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 20-gonal numbers.
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LINKS
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FORMULA
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a(2n) = 16*n, a(2n+1) = 2*n + 1.
G.f.: x*(1 + 16*x + x^2) / ((1 - x)^2*(1 + x)^2).
a(n) = 2*a(n-2) - a(n-4) for n>3. (End)
Multiplicative with a(2^e) = 2^(e+3), and a(p^e) = p^e for an odd prime p. - Amiram Eldar, Oct 14 2023
Dirichlet g.f.: zeta(s-1) * (1 + 7*2^(1-s)). - Amiram Eldar, Oct 25 2023
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MATHEMATICA
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a[n_] := If[OddQ[n], n, 8*n]; Array[a, 70, 0] (* Amiram Eldar, Oct 14 2023 *)
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PROG
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(PARI) concat(0, Vec(x*(1 + 16*x + x^2) / ((1 - x)^2*(1 + x)^2) + O(x^60))) \\ Colin Barker, Jul 29 2018
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CROSSREFS
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KEYWORD
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nonn,easy,mult
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AUTHOR
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STATUS
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approved
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