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A290052
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Number of X-rays of n X n binary matrices with exactly n ones.
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4
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1, 1, 4, 23, 139, 860, 5393, 34142, 217717, 1396346, 8997695, 58205686, 377775385, 2458841504, 16043226825, 104901986083, 687221188145, 4509605878736, 29636894936761, 195035340954186, 1285062484293880, 8476508261617168, 55969236979211755, 369900194873712830
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OFFSET
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0,3
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COMMENTS
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The X-ray of a matrix is defined as the sequence of antidiagonal sums.
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LINKS
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FORMULA
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a(n) ~ c * 3^(3*n) / (2^(2*n) * sqrt(n)), where c = 0.153294749730773567280925277269616968259180871352428154276351832424636097919... - Vaclav Kotesovec, Jul 22 2017
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EXAMPLE
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a(0) = 1: [].
a(1) = 1: 1.
a(2) = 4: 011, 020, 101, 110.
a(3) = 23: 00021, 00111, 00120, 00201, 00210, 00300, 01011, 01020, 01101, 01110, 01200, 02001, 02010, 02100, 10011, 10020, 10101, 10110, 10200, 11001, 11010, 11100, 12000.
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MAPLE
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b:= proc(n, i, t) option remember; (m-> `if`(n>m, 0, `if`(n=m, 1,
add(b(n-j, i-t, 1-t), j=0..min(i, n)))))(i*(i+1-t))
end:
a:= n-> b(n$2, 1):
seq(a(n), n=0..30);
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MATHEMATICA
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b[n_, i_, t_] := b[n, i, t] = Function[m, If[n > m, 0, If[n == m, 1, Sum[b[n - j, i - t, 1 - t], {j, 0, Min[i, n]}]]]][i*(i + 1 - t)];
a[n_] := b[n, n, 1];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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