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%I #13 Jun 24 2017 13:44:52
%S 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,
%T 1,19,91,193,193,91,19,1,1,22,127,346,481,346,127,22,1,1,25,169,565,
%U 1021,1021,565,169,25,1,1,28,217,862,1933,2524,1933,862
%N 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).
%p 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;
%t 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 *)
%Y Main diagonal is A027618. Rows give A003215, A047672, A047673, A047674.
%Y a(n, k) = A008288(n-1, k-1) + A047662(n-1, k-1).
%K nonn,tabl,nice,easy
%O 1,5
%A _N. J. A. Sloane_
%E Description corrected by _Henry Bottomley_, May 09 2000
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