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A195140
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Multiples of 5 and odd numbers interleaved.
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23
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0, 1, 5, 3, 10, 5, 15, 7, 20, 9, 25, 11, 30, 13, 35, 15, 40, 17, 45, 19, 50, 21, 55, 23, 60, 25, 65, 27, 70, 29, 75, 31, 80, 33, 85, 35, 90, 37, 95, 39, 100, 41, 105, 43, 110, 45, 115, 47, 120, 49, 125, 51, 130, 53, 135, 55, 140, 57, 145, 59, 150, 61, 155, 63
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OFFSET
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0,3
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COMMENTS
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This is 5*n/2 if n is even, n if n is odd.
Partial sums give the generalized enneagonal numbers A118277.
a(n) is also the length of the n-th line segment of a rectangular spiral on the infinite square grid. The vertices of the spiral are the generalized enneagonal numbers. - Omar E. Pol, Jul 27 2018
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LINKS
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FORMULA
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a(2n) = 5n, a(2n+1) = 2n+1.
G.f.: x*(1+5*x+x^2) / ((x-1)^2*(x+1)^2). - Alois P. Heinz, Sep 26 2011
a(n) = (7+3*(-1)^n)*n/4.
a(n) = -a(-n) = a(n-2)*n/(n-2) = 2*a(n-2)-a(n-4).
Multiplicative with a(2^e) = 5*2^(e-1), a(p^e) = p^e for odd prime p. - Andrew Howroyd, Jul 23 2018
Dirichlet g.f.: zeta(s-1) * (1 + 3/2^s). - Amiram Eldar, Oct 25 2023
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MATHEMATICA
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With[{nn=40}, Riffle[5*Range[0, nn], Range[1, 2nn+1, 2]]] (* or *) LinearRecurrence[ {0, 2, 0, -1}, {0, 1, 5, 3}, 80] (* Harvey P. Dale, Dec 15 2014 *)
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PROG
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(Magma) &cat[[5*n, 2*n+1]: n in [0..31]]; // Bruno Berselli, Sep 27 2011
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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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EXTENSIONS
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STATUS
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approved
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