A019463 Add 1, multiply by 1, add 2, multiply by 2, etc., start with 1.

1, 2, 2, 4, 8, 11, 33, 37, 148, 153, 765, 771, 4626, 4633, 32431, 32439, 259512, 259521, 2335689, 2335699, 23356990, 23357001, 256927011, 256927023, 3083124276, 3083124289, 40080615757, 40080615771, 561128620794, 561128620809, 8416929312135, 8416929312151, 134670868994416

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..900

Nick Hobson, Python program for this sequence.

Formula

Limit_{n->oo} a(2n)/n! = 1 + 2e = 1 + A019762. - Jon E. Schoenfield, Jan 16 2024

Maple

a:= proc(n) option remember; `if`(n=0, 1, (t->
      `if`(n::odd, t+(n+1)/2, t*n/2))(a(n-1)))
    end:
seq(a(n), n=0..32);  # Alois P. Heinz, Jan 16 2024

Mathematica

For[i=1; lst={1}, i<15, i++, AppendTo[lst, i+Last[lst]]; AppendTo[lst, i Last[lst]]]; lst (* Harvey P. Dale, Feb 25 2012 *)
FoldList[If[OddQ[#2], #1 + (#2 + 1)/2, #1 * (#2/2)]&, 1, Range[32]] (* AnneMarie Torresen, Nov 26 2023 *)

Prog

(PARI) A019463(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. A019461 (same, but start with 0), A019460 (start with 2), A019462, (start with 3), A082448. (start with 4).

Cf. A082458, A019464, A019465, A019466 (similar, but first multiply, then add).

Cf. A019762.

Sequence in context: A056381 A245597 A324039 * A152763 A221666 A086700

Adjacent sequences: A019460 A019461 A019462 * A019464 A019465 A019466

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Edited by M. F. Hasler, Feb 25 2018

Status

approved