A019464 Multiply by 1, add 1, multiply by 2, add 2, etc., start with 1.

1, 1, 2, 4, 6, 18, 21, 84, 88, 440, 445, 2670, 2676, 18732, 18739, 149912, 149920, 1349280, 1349289, 13492890, 13492900, 148421900, 148421911, 1781062932, 1781062944, 23153818272, 23153818285, 324153455990, 324153456004, 4862301840060, 4862301840075, 77796829441200

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A033540 (=a(2n)).

Cf. A082458 (same, but start with 0), A019465 (start with 2), A019466 (start with 3).

Cf. A019460 .. A019463 & A082448 (similar, but first add, then multiply).

Programs

Haskell

a019464 n = a019464_list !! n
a019464_list = 1 : concat (unfoldr ma (1, [1, 1])) where
   ma (x, [_, j]) = Just (ij', (x + 1, ij')) where ij' = [x * j, x * j + x]
-- Reinhard Zumkeller, Nov 14 2011

Mathematica

a[n_?EvenQ] := n/2 + a[n-1]; a[n_?OddQ] := (n+1)*a[n-1]/2;
a[0] = 1; Table[a[n], {n, 0, 27}] (* Jean-François Alcover, Nov 15 2011 *)

PARI

A019464(n,a=1)={for(i=2,n+1,if(bittest(i,0),a+=i\2,a*=i\2));a} \\ M. F. Hasler, Feb 25 2018

Formula

For n>=1, a(2n)=floor((1+e)*(n-1)!)-1, a(2n+1)=floor((1+e)*(n+1)!)-n-2. - Benoit Cloitre, Apr 29 2003

a(n+1) = (1/2)*a(n)*(n+1 mod 2)*(n+2) + (1/2)*(n mod 2)*(2*a(n)+n+1). - Francois Jooste (pin(AT)myway.com), Jun 25 2003

a(n) = (n mod 2)*(floor((1+e)*(floor(n/2)+1)!)-floor(n/2)-2)+((n+1) mod 2)*(floor((1+e)*floor(n/2)!)-1) for n >= 1 with a(0) = 1. - Wesley Ivan Hurt, Aug 04 2025

Extensions

Edited by M. F. Hasler, Feb 25 2018