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A047666
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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).
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5
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| T(n, m)=Sum{1 <= i <= n-m}[(2*i+1)*U(n-i-1, m-1)] + Sum{1 <= i <= m} [(2*i+1)*U(n-2, m-i)] - U(n-2, m-1) with U(n, m)=A008288(n, m). - Floor van Lamoen (fvlamoen(AT)hotmail.com), Aug 16 2001
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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;
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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}]] (* From Jean-François Alcover, Feb 10 2012 *)
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CROSSREFS
| Main diagonal is A002002. Rows give A002522, A047667, A047668, ...
Sequence in context: A196957 A124727 A125101 * A196696 A196729 A197069
Adjacent sequences: A047663 A047664 A047665 * A047667 A047668 A047669
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KEYWORD
| nonn,tabl,nice,easy,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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