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A317318
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Multiples of 18 and odd numbers interleaved.
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4
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0, 1, 18, 3, 36, 5, 54, 7, 72, 9, 90, 11, 108, 13, 126, 15, 144, 17, 162, 19, 180, 21, 198, 23, 216, 25, 234, 27, 252, 29, 270, 31, 288, 33, 306, 35, 324, 37, 342, 39, 360, 41, 378, 43, 396, 45, 414, 47, 432, 49, 450, 51, 468, 53, 486, 55, 504, 57, 522, 59, 540, 61, 558, 63, 576, 65, 594, 67, 612, 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 22-gonal numbers (A303299).
a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 22-gonal numbers.
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LINKS
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FORMULA
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a(2n) = 18*n, a(2n+1) = 2*n + 1.
G.f.: x*(1 + 18*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) = 9*2^e, and a(p^e) = p^e for an odd prime p. - Amiram Eldar, Oct 14 2023
Dirichlet g.f.: zeta(s-1) * (1 + 2^(4-s)). - Amiram Eldar, Oct 25 2023
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MATHEMATICA
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a[n_] := If[OddQ[n], n, 9*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 + 18*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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