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A080512

a(n) = n if n is odd, a(n) = 3*n/2 if n is even.

1, 3, 3, 6, 5, 9, 7, 12, 9, 15, 11, 18, 13, 21, 15, 24, 17, 27, 19, 30, 21, 33, 23, 36, 25, 39, 27, 42, 29, 45, 31, 48, 33, 51, 35, 54, 37, 57, 39, 60, 41, 63, 43, 66, 45, 69, 47, 72, 49, 75, 51, 78, 53, 81, 55, 84, 57, 87, 59, 90, 61, 93, 63, 96, 65, 99, 67, 102

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OFFSET

1,2

COMMENTS

First differences of the generalized heptagonal numbers A085787. - Omar E. Pol, Sep 10 2011

Last term in n-th row of A080511.

Also A005408 and positive terms of A008585 interleaved. - Omar E. Pol, May 28 2012

a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized heptagonal numbers. - Omar E. Pol, Jul 27 2018

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

FORMULA

a(n) = n if n is odd, a(n) = 3*n/2 if n is even.

a(n)*a(n+3) = -3 + a(n+1)*a(n+2).

From Paul Barry, Sep 04 2003: (Start)

G.f.: (1+3*x+x^2)/((1-x^2)^2);

a(n) = n*(5 + (-1)^n)/4. (End)

Multiplicative with a(2^e) = 3*2^(e-1), a(p^e) = p^e otherwise. - Christian G. Bower, May 17 2005

Equals A126988 * (1, 1, 0, 0, 0, ...) - Gary W. Adamson, Apr 17 2007

Dirichlet g.f.: zeta(s-1) * (1 + 1/2^s). - Amiram Eldar, Oct 25 2023