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A047671
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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).
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5
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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
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table;
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refs;
listen;
history;
text;
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OFFSET
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1,5
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LINKS
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Table of n, a(n) for n=1..63.
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MAPLE
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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;
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MATHEMATICA
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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 *)
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CROSSREFS
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Main diagonal is A027618. Rows give A003215, A047672, A047673, A047674.
a(n, k) = A008288(n-1, k-1) + A047662(n-1, k-1).
Sequence in context: A157172 A131060 A124376 * A081577 A146986 A304141
Adjacent sequences: A047668 A047669 A047670 * A047672 A047673 A047674
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KEYWORD
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nonn,tabl,nice,easy
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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Description corrected by Henry Bottomley, May 09 2000
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STATUS
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approved
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