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

0,3

Links

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

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

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 *)

Prog

(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
(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

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).

Sequence in context: A074131 A355078 A335038 * A064402 A268577 A075229

Adjacent sequences: A019461 A019462 A019463 * A019465 A019466 A019467

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

Edited by M. F. Hasler, Feb 25 2018

Status

approved