

A080512


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


34



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

Multiplicative with a(2^e) = 3*2^(e1), a(p^e) = p^e otherwise.  Christian G. Bower, May 17 2005
First differences of the generalized heptagonal numbers A085787.  Omar E. Pol, Sep 10 2011
Last term in nth 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 nth 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


FORMULA

a(n) = n if n is odd, a(n) = 3*n/2 if n is even.
From Paul Barry, Sep 04 2003: (Start)
G.f.: (1+3*x+x^2)/((1x^2)^2);
a(n) = n*(5 + (1)^n)/4. (End)
a(n)*a(n+3) = 3 + a(n+1)*a(n+2).
Equals A126988 * (1, 1, 0, 0, 0, ...)  Gary W. Adamson, Apr 17 2007


MATHEMATICA

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


PROG

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


CROSSREFS

Cf. A080511, A008619, A126988.
Cf. A064455, A085787.
Sequence in context: A295220 A280167 A257143 * A225441 A102245 A038167
Adjacent sequences: A080509 A080510 A080511 * A080513 A080514 A080515


KEYWORD

nonn,easy,mult


AUTHOR

Amarnath Murthy, Mar 20 2003


STATUS

approved



