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

Offset: 1

Author

Amarnath Murthy, Mar 20 2003

Keywords

• nonn
• easy
• mult

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).

Crossrefs

Cf. A080511, A008619, A126988.

Cf. A005408, A008585, A064455, A085787, A126246

Programs

Haskell

import Data.List (transpose)
a080512 n = if m == 0 then 3 * n' else n  where (n', m) = divMod n 2
a080512_list = concat $ transpose [[1, 3 ..], [3, 6 ..]]
-- Reinhard Zumkeller, Apr 06 2015

Magma

[n*(5+(-1)^n)/4: n in [1..60]]; // Vincenzo Librandi, Sep 11 2011

Mathematica

Table[If[EvenQ[n],3n/2,n],{n,68}] (* Jayanta Basu, May 20 2013 *)

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

Sum_{d divides n} mu(n/d)*a(d) = A126246(n), where mu(n) = A008683(n) is the Möbius function. - Peter Bala, Dec 31 2023