A259842 Number of nonzero elements in all n X n Tesler matrices of nonnegative integers.

1, 4, 22, 178, 2114, 36398, 896128, 31136246, 1508259823, 100727634758, 9179951931947, 1131033520118692, 186769092227016256, 41008206412935719870, 11884278052476825052541, 4514826724675651497522250, 2234142899928806917974566378, 1431533853656098851281985968328

Offset

1,2

Comments

For the definition of Tesler matrices see A008608.

Links

Table of n, a(n) for n=1..18.

Formula

a(n) = Sum_{k=1..n} A259841(n,k).

Example

There are two 2 X 2 Tesler matrices: [1,0; 0,1], [0,1; 0,2], containing four nonzero elements, thus a(2) = 4.

Maple

g:= u-> `if`(u=0, 0, 1):
b:= proc(n, i, l) option remember; (m->`if`(m=0, [1, g(n)], `if`(i=0,
     (p->p+[0, p[1]*g(n)])(b(l[1]+1, m-1, subsop(1=NULL, l))), add(
     (p->p+[0, p[1]*g(j)])(b(n-j, i-1, subsop(i=l[i]+j, l)))
      , j=0..n))))(nops(l))
    end:
a:= n-> b(1, n-1, [0$(n-1)])[2]:
seq(a(n), n=1..14);

Mathematica

g[u_] := If[u == 0, 0, 1];
b[n_, i_, l_] := b[n, i, l] = Function[m, If[m == 0, {1, g[n]}, If[i == 0,
     # + {0, #[[1]] g[n]}&[b[l[[1]] + 1, m - 1, ReplacePart[l, 1 ->
     Nothing]]], Sum[# + {0, #[[1]] g[j]}&[b[n - j, i - 1, ReplacePart[
     l, i -> l[[i]] + j]]], {j, 0, n}]]]][Length[l]];
a[n_] := b[1, n - 1, Table[0, {n - 1}]][[2]];
Table[Print[n, " ", a[n]]; a[n], {n, 1, 18}] (* Jean-François Alcover, May 15 2022, after Alois P. Heinz *)

Crossrefs

Row sums of A259841.

Cf. A008608.

Sequence in context: A207654 A197923 A294343 * A125863 A004115 A362747

Adjacent sequences: A259839 A259840 A259841 * A259843 A259844 A259845

Keyword

nonn

Author

Alois P. Heinz, Jul 06 2015

Status

approved