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 A129853 Nonascending wiggly sums: number of sums adding to n in which terms alternately do not increase and do not decrease. 2
 1, 2, 3, 6, 9, 17, 28, 50, 85, 149, 257, 448, 775, 1347, 2336, 4057, 7038, 12219, 21204, 36807, 63880, 110878, 192442, 334020, 579739, 1006237, 1746482, 3031310, 5261324, 9131892, 15849876, 27510049, 47748159, 82874713, 143842547, 249662173, 433329337, 752113633, 1305415658, 2265761441 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS EXAMPLE The a(4)=6 sums that add to 4 are 4, 3+1, 2+2, 2+1+1, 1+1+2 and 1+1+1+1. The 2 = 2^(n-1)-a(n) sums 1+2+1 and 1+3 do not satisfy the criterion and do not count. From Joerg Arndt, May 21 2013: (Start) The a(6)=17 such compositions are 01:  [ 1 1 1 1 1 1 ] 02:  [ 1 1 1 1 2 ] 03:  [ 1 1 2 1 1 ] 04:  [ 1 1 2 2 ] 05:  [ 1 1 3 1 ] 06:  [ 1 1 4 ] 07:  [ 2 1 1 1 1 ] 08:  [ 2 1 2 1 ] 09:  [ 2 1 3 ] 10:  [ 2 2 2 ] 11:  [ 3 1 1 1 ] 12:  [ 3 1 2 ] 13:  [ 3 3 ] 14:  [ 4 1 1 ] 15:  [ 4 2 ] 16:  [ 5 1 ] 17:  [ 6 ] (End) MAPLE A129853rec := 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 = 0 then for k from op(-1, part) to n-asum do a := a+A129853rec([op(part), k], n) ; od: else for k from 1 to min(op(-1, part), n-asum) do a := a+A129853rec([op(part), k], n) ; od: fi ; RETURN(a) ; fi ; end: A129853 := proc(n) local a, a1 ; a := 0 ; for a1 from 1 to n do a := a+A129853rec([a1], n) ; od: RETURN(a) ; end: seq(A129853(n), n=1..20) ; # R. J. Mathar, Oct 31 2007 CROSSREFS Cf. A129852. Cf. A025048, A025049. Sequence in context: A048815 A074045 A073776 * A095982 A095090 A061947 Adjacent sequences:  A129850 A129851 A129852 * A129854 A129855 A129856 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 STATUS approved

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Last modified April 3 22:30 EDT 2020. Contains 333207 sequences. (Running on oeis4.)