A047666 Square array a(n,k) read by antidiagonals: a(n,1)=n, a(1,k)=k, a(n,k) = a(n-1,k-1) + a(n-1,k) + a(n,k-1).

1, 2, 2, 3, 5, 3, 4, 10, 10, 4, 5, 17, 25, 17, 5, 6, 26, 52, 52, 26, 6, 7, 37, 95, 129, 95, 37, 7, 8, 50, 158, 276, 276, 158, 50, 8, 9, 65, 245, 529, 681, 529, 245, 65, 9, 10, 82, 360, 932, 1486, 1486, 932, 360, 82, 10, 11, 101, 507, 1537, 2947, 3653

Offset

1,2

Links

Table of n, a(n) for n=1..61.

Formula

T(n, m) = (Sum_{i=1..n-m}(2*i+1)*U(n-i-1, m-1)) + (Sum_{i=1..m} (2*i+1)*U(n-2, m-i)) - U(n-2, m-1) where U(n, m) = A008288(n, m). - Floor van Lamoen, Aug 16 2001

Maple

A047666 := proc(n, k) option remember; if n = 1 then k; elif k = 1 then n; else A047666(n-1, k-1)+A047666(n, k-1)+A047666(n-1, k); fi; end;

Mathematica

nmax = 11; a[1, k_] := k; a[n_, 1] := n; a[n_, k_] := a[n, k] = a[n-1, k-1] + a[n, k-1] + a[n-1, k]; Flatten[ Table[ a[n-k+1, k], {n, 1, nmax}, {k, 1, n}]] (* Jean-François Alcover, Feb 10 2012 *)

Crossrefs

Main diagonal is A002002. Rows give A002522, A047667, A047668, ...

Sequence in context: A208519 A336725 A210232 * A285935 A209568 A227641

Adjacent sequences: A047663 A047664 A047665 * A047667 A047668 A047669

Keyword

nonn,tabl,nice,easy

Author

N. J. A. Sloane

Status

approved