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%I #17 Jun 24 2017 23:22:25
%S 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,
%T 7,8,50,158,276,276,158,50,8,9,65,245,529,681,529,245,65,9,10,82,360,
%U 932,1486,1486,932,360,82,10,11,101,507,1537,2947,3653
%N 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).
%F 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
%p 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;
%t 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 *)
%Y Main diagonal is A002002. Rows give A002522, A047667, A047668, ...
%K nonn,tabl,nice,easy
%O 1,2
%A _N. J. A. Sloane_
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