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A068602 Number of functions f:{0,1,2,...,n} -> {0,1,2,...,n} that satisfy f(0)=0 and f(n)=0, with f nowhere concave upward. 0
1, 1, 3, 8, 23, 54, 137, 297, 659, 1355, 2765, 5332, 10315, 19040, 34917, 62302, 110129, 190065, 325844, 547683, 913936, 1502371, 2450281, 3945459, 6312470, 9986624, 15696792, 24445887, 37838409, 58085458, 88678438 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..30.

EXAMPLE

a(3)=8 since the following 4-tuples of function values (f(0),f(1),f(2),f(3)) and no others, have the required properties: (0,0,0,0), (0,1,1,0), (0,1,2,0), (0,2,1,0), (0,2,2,0), (0,2,3,0), (0,3,2,0) and (0,3,3,0).

PROG

{Pascal} program concave1; var n:integer; function f(y0, x1, y1, n:integer): longint; var y, ymax:integer; ct:longint; begin if n=0 then begin f := 1; exit; end; if x1=n-1 then begin f := 1; exit; end; ct := 0; if x1=0 then ymax := n else ymax := 2*y1-y0; if ymax>n then ymax := n; for y := y1-(y1 div (n-x1)) to ymax do ct := ct+f(y1, x1+1, y, n); f := ct; end; begin for n := 0 to 30 do write(f(0, 0, 0, n):10); readln; end.

CROSSREFS

Sequence in context: A183922 A340493 A296286 * A255834 A027212 A027236

Adjacent sequences:  A068599 A068600 A068601 * A068603 A068604 A068605

KEYWORD

nonn

AUTHOR

John W. Layman, Mar 28 2002

STATUS

approved

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Last modified October 18 06:50 EDT 2021. Contains 348066 sequences. (Running on oeis4.)