The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A183157

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A183157

Triangle read by rows: T(n,k) is the number of partial isometries of an n-chain of height k (height of alpha = |Im(alpha)|).
(history; published version)

#22 by Michel Marcus at Sun Jan 06 04:07:26 EST 2019

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reviewed

approved

#21 by Joerg Arndt at Sun Jan 06 04:06:37 EST 2019

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proposed

reviewed

#20 by Jon E. Schoenfield at Sun Jan 06 04:02:06 EST 2019

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editing

proposed

#19 by Jon E. Schoenfield at Sun Jan 06 04:02:03 EST 2019

NAME

Triangle read by rows: T(n,k) is the number of partial isometries (of an n-chain) of height k (height of alpha = |Im(alpha)|).

FORMULA

T(n,0)=1, T(n,1) = n^2 and T(n,k)=2*(2*n-k+1)*binomial(n,k)/(k+1), (k > 1).

EXAMPLE

1.;

1...., 1.;

1...., 4...., 2.;

1...., 9..., 10...., 2.;

1..., 16..., 28..., 12...., 2.;

1..., 25..., 60..., 40..., 14...., 2.;

1..., 36.., 110.., 100..., 54..., 16...., 2.;

1..., 49.., 182.., 210.., 154..., 70..., 18...., 2.;

1..., 64.., 280.., 392.., 364.., 224..., 88..., 20...., 2.;

1..., 81.., 408.., 672.., 756.., 588.., 312.., 108..., 22...., 2.;

1.., 100.., 570., 1080., 1428., 1344.., 900.., 420.., 130..., 24...., 2.;

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approved

editing

#18 by Alois P. Heinz at Sat Nov 25 16:30:16 EST 2017

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reviewed

approved

#17 by Wesley Ivan Hurt at Sat Nov 25 16:28:03 EST 2017

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proposed

reviewed

#16 by Jean-François Alcover at Sat Nov 25 12:28:31 EST 2017

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editing

proposed

#15 by Jean-François Alcover at Sat Nov 25 12:28:26 EST 2017

MATHEMATICA

T[_, 0] = 1; T[n_, 1] := n^2; T[n_, k_] := 2*(2*n - k + 1)*Binomial[n, k] / (k + 1);

Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Nov 25 2017 *)

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approved

editing

#14 by N. J. A. Sloane at Sat Jun 03 20:57:34 EDT 2017

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proposed

approved

#13 by Michel Marcus at Sat Jun 03 16:27:54 EDT 2017

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editing

proposed