A259787 Total element sum of all n X n Tesler matrices of nonnegative integers.

1, 5, 31, 270, 3370, 60146, 1522031, 54055976, 2666453502, 180847717069, 16704822358932, 2082808024263350, 347639192485104658, 77076883307827211845, 22537752778732740525833, 8633258320969387044105210, 4305220991520242104331411368, 2778601200692503839128415662124

Offset

1,2

Comments

For the definition of Tesler matrices see A008608.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..21

Formula

a(n) = Sum_{k=0..n*(n-1)/2} (n+k) * A259786(n,k).

a(n) = Sum_{k=0..n} k * A259841(n,k).

Example

There are two 2 X 2 Tesler matrices: [1,0; 0,1], [0,1; 0,2], the total sum of all elements gives a(2) = 5.

Maple

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

Mathematica

b[n_, i_, l_] := b[n, i, l] = Function[m, If[m == 0, {1, 0}, If[i == 0, Function[p, p + {0, p[[1]]*(l[[1]] + 1)}][b[l[[1]] + 1, m - 1, ReplacePart[l, 1 -> Nothing]]], Sum[b[n - j, i - 1, ReplacePart[l, i -> l[[i]] + j]], {j, 0, n}]]]][Length[l]];
a[n_] := Function[p, p[[1]] + p[[2]]][b[1, n - 1, Table[0, {n - 1}]]];
Table[a[n], {n, 1, 14}] (* Jean-François Alcover, Jun 27 2022, after Alois P. Heinz *)

Crossrefs

Cf. A008608, A259786, A259841.

Sequence in context: A058892 A177453 A346405 * A273601 A218679 A296967

Adjacent sequences: A259784 A259785 A259786 * A259788 A259789 A259790

Keyword

nonn

Author

Alois P. Heinz, Jul 05 2015

Status

approved