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A047922
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Triangle of numbers a(n,k) = number of terms in n X n determinant with 2 adjacent diagonals of k and k-1 0's (0<=k<=n).
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5
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1, 1, 0, 2, 1, 0, 6, 4, 1, 1, 24, 18, 8, 5, 3, 120, 96, 54, 34, 23, 16, 720, 600, 384, 258, 182, 131, 96, 5040, 4320, 3000, 2136, 1566, 1168, 883, 675, 40320, 35280, 25920, 19320, 14664, 11274, 8756, 6859, 5413, 362880, 322560, 246960, 190800, 149160, 117696, 93582, 74902, 60301, 48800
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OFFSET
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0,4
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LINKS
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FORMULA
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Right diagonal is A000271, column k=0 is A000142; other entries given by a(n, k) = a(n, k+1) + 2a(n-1, k) + a(n-2, k-1).
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EXAMPLE
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Triangle starts:
1;
1, 0;
2, 1, 0;
6, 4, 1, 1;
...
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MAPLE
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a:= proc(n, k) option remember; `if`(k=0, n!, `if`(n=k,
`if`(n<3, (n-1)*(n-2)/2, (n-1)*(a(n-1$2)+a(n-2$2))
+a(n-3$2)), a(n, k+1) +2*a(n-1, k) +a(n-2, k-1)))
end:
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MATHEMATICA
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a[n_, n_] := (-1)^n*HypergeometricPFQ[{1, -n, n+1}, {1/2}, 1/4]; a[n_, k_] := a[n, k] = a[n, k+1] + 2*a[n-1, k] + a[n-2, k-1]; Table[a[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jun 24 2015 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Sep 29 2000
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STATUS
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approved
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