A129852 Nondescending wiggly sums: number of sums adding to n in which terms alternately do not decrease and do not increase.

1, 1, 2, 3, 5, 9, 15, 26, 45, 79, 135, 236, 408, 710, 1230, 2137, 3705, 6436, 11165, 19384, 33637, 58391, 101336, 175896, 305284, 529884, 919683, 1596277, 2770576, 4808811, 8346446, 14486644, 25143896, 43641363, 75746646, 131470683, 228188723, 396058740, 687424365, 1193136983, 2070883422

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..2000

Example

From Joerg Arndt, May 21 2013: (Start)
The a(6)=15 such compositions are
01:  [ 1 1 1 1 1 1 ]
02:  [ 1 1 1 2 1 ]
03:  [ 1 1 1 3 ]
04:  [ 1 2 1 1 1 ]
05:  [ 1 2 1 2 ]
06:  [ 1 3 1 1 ]
07:  [ 1 3 2 ]
08:  [ 1 4 1 ]
09:  [ 1 5 ]
10:  [ 2 2 1 1 ]
11:  [ 2 2 2 ]
12:  [ 2 3 1 ]
13:  [ 2 4 ]
14:  [ 3 3 ]
15:  [ 6 ]
(End)

Maple

A129852rec := proc(part, n) local asum, a, k ; asum := add(i, i=part) ; if asum > n then RETURN(0) ; elif asum = n then RETURN(1) ; else a := 0 ; if nops(part) mod 2 = 1 then for k from op(-1, part) to n-asum do a := a+A129852rec([op(part), k], n) ; od: else for k from 1 to min(op(-1, part), n-asum) do a := a+A129852rec([op(part), k], n) ; od: fi ; RETURN(a) ; fi ; end: A129852 := proc(n) local a, a1 ; a := 0 ; for a1 from 1 to n do a := a+A129852rec([a1], n) ; od: RETURN(a) ; end: seq(A129852(n), n=1..20) ; # R. J. Mathar, Oct 31 2007
# second Maple program:
b:= proc(n, l, t) option remember; `if`(n=0, 1, add(
      b(n-j, j, not t), j=`if`(t, l..n, 1..min(n, l))))
    end:
a:= n-> b(n$2, false):
seq(a(n), n=0..40);  # Alois P. Heinz, May 23 2023

Mathematica

b[n_, l_, t_] := b[n, l, t] = If[n == 0, 1, Sum[b[n-j, j, !t], {j, If[t, Range[l, n], Range[Min[n, l]]]}]];
a[n_] := b[n, n, False];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, May 23 2023, after Alois P. Heinz *)

Crossrefs

Cf. A129853.

Cf. A025048, A025049.

Sequence in context: A185649 A005169 A338192 * A367666 A065954 A067847

Adjacent sequences: A129849 A129850 A129851 * A129853 A129854 A129855

Keyword

nonn

Author

Vladeta Jovovic, May 22 2007

Extensions

More terms from R. J. Mathar, Oct 31 2007

More terms from Joerg Arndt, May 21 2013

a(0)=1 prepended by Alois P. Heinz, May 23 2023

Status

approved