A047671 Square array a(n,k) read by antidiagonals: a(n,1)=1, a(1,k)=1, a(n,k) = 1 + a(n-1,k-1) + a(n-1,k) + a(n,k-1).

1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 10, 19, 10, 1, 1, 13, 37, 37, 13, 1, 1, 16, 61, 94, 61, 16, 1, 1, 19, 91, 193, 193, 91, 19, 1, 1, 22, 127, 346, 481, 346, 127, 22, 1, 1, 25, 169, 565, 1021, 1021, 565, 169, 25, 1, 1, 28, 217, 862, 1933, 2524, 1933, 862

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• tabl
• nice
• easy

Crossrefs

Main diagonal is A027618. Rows give A003215, A047672, A047673, A047674.

a(n, k) = A008288(n-1, k-1) + A047662(n-1, k-1).

Programs

Maple

A047671 := proc(n,k) option remember; if n = 1 then 1; elif k = 1 then 1; else 1+A047671(n-1,k-1)+A047671(n,k-1)+A047671(n-1,k); fi; end;

Mathematica

nmax = 12; a[, 1] = 1; a[1, ] = 1; a[n_ /; n > 1, k_ /; k > 1] :=  a[n, k] = 1 + a[n-1, k-1] + a[n-1, k] + a[n, k-1]; Flatten[ Table[ a[n-k , k], {n, 1, nmax}, {k, 1, n-1}]] (* Jean-François Alcover, Jul 19 2012 *)

Extensions

Description corrected by Henry Bottomley, May 09 2000