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A086753 Number of distinct entries in a slice of A046816. 2
1, 1, 2, 3, 4, 5, 7, 8, 9, 12, 13, 16, 19, 21, 24, 25, 30, 32, 37, 40, 43, 46, 51, 56, 59, 64, 67, 75, 79, 83, 91, 93, 102, 108, 111, 119, 125, 131, 139, 147, 154, 160, 167, 175, 183, 189, 199, 206, 214, 225, 233, 243, 250, 261, 268, 279, 289, 298, 309, 317 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..800

EXAMPLE

The slice for n=4 is

      1

     4 4

    6 12 6

   4 12 12 4

  1 4  6  4 1

with distinct entries 1,4,6,12, so a(4) = 4.

MAPLE

p:= proc(i, j, k) option remember;

      if i<0 or j<0 or k<0 or i>k or j>i then 0

    elif {i, j, k}={0} then 1

    else p(i, j, k-1) +p(i-1, j, k-1) +p(i-1, j-1, k-1)

      fi

    end:

a:= n-> nops({seq(seq(p(i, j, n), j=0..i), i=0..n)}):

seq(a(n), n=0..50);  # Alois P. Heinz, Aug 14 2012

#

seq(nops({coeffs(expand((x+y+z)^n))}), n = 0 .. 100); # César Eliud Lozada, Jul 02 2015

#

seq(nops({seq(seq(n!/(i!*j!*(n-i-j)!), j=i..(n-i)/2), i=0..n/3)}), n=0..100); # Robert Israel, Jul 02 2015

MATHEMATICA

Table[Length @ Union @ Flatten @ Table[Table[n!/(i!*j!*(n-i-j)!), {j, i, (n-i)/2}], {i, 0, n/3}], {n, 0, 100}] (* Jean-François Alcover, Mar 19 2019, after Robert Israel *)

PROG

(PARI) { pt=vector(40, i, matrix(i, i)); pt[1][1, 1]=1; pt[2][1, 1]=1; pt[2][2, 1]=1; pt[2][2, 2]=1; pt[3][1, 1]=1; pt[3][2, 1]=2; pt[3][2, 2]=2; pt[3][3, 1]=1; pt[3][3, 2]=2; pt[3][3, 3]=1; for (i=4, 40, for (j=2, i-1, pt[i][j, 1]=pt[i-1][j-1, 1]+pt[i-1][j, 1]; pt[i][j, j]=pt[i][j, 1]; pt[i][i, j]=pt[i][j, 1] ); pt[i][1, 1]=1; pt[i][i, 1]=1; pt[i][i, i]=1; for(j=3, i-1, for (k=2, j-1, pt[i][j, k]=pt[i-1][j, k]+pt[i-1][j-1, k]+pt[i-1][j-1, k-1]))); pt } { makept(x)=local(xl, v, vc, uc); xl=length(x); v=vector(xl*(xl+1)/2); vc=0; for (i=1, xl, for (j=1, i, v[vc++ ]=x[i, j])); v=vecsort(v); uc=1; for (i=2, length(v), if (v[i]!=v[i-1], uc++)); print1(", "uc) } for (i=1, 40, makept(pt([i]))

CROSSREFS

Cf. A046816.

Sequence in context: A192140 A084092 A288927 * A160519 A287927 A241480

Adjacent sequences:  A086750 A086751 A086752 * A086754 A086755 A086756

KEYWORD

nonn

AUTHOR

Jon Perry, Jul 31 2003

EXTENSIONS

More terms from Alois P. Heinz, Aug 14 2012

STATUS

approved

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Last modified December 13 22:48 EST 2019. Contains 329974 sequences. (Running on oeis4.)