Revision History for A050166
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#55 by Charles R Greathouse IV at Thu Sep 08 08:44:58 EDT 2022
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| PROG
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(MAGMAMagma) [[2*(n-k+1)*Binomial(2*n+1, k)/(2*n-k+2): k in [0..n]]: n in [0..10]]; // G. C. Greubel, Apr 05 2019
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Discussion
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| Thu Sep 08
| 08:44
| OEIS Server: https://oeis.org/edit/global/2944
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#54 by Alois P. Heinz at Tue Jan 21 21:20:23 EST 2020
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#53 by Jon E. Schoenfield at Tue Jan 21 21:18:10 EST 2020
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#52 by Jon E. Schoenfield at Tue Jan 21 21:18:07 EST 2020
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| COMMENTS
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Given (1) = row 0, then the sum of terms with alternating signs in row r of A050166 = (-1)^r * A000108(n); where A000108 = 1, 1, 2, 5, 14, 42..., ...the Catalan numbers. - Herb Conn
The diagonals of this triangle are self-convolutions of the main diagonal A000108(n+1) : ): 1, 2, 5, 14, 42, 132, 429, . . . - _, ... - _Philippe Deléham_, May 25 2005
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| FORMULA
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T(n, k) = T(n-1, k) + 2*T(n-1, k-1) + T(n-1, k-2), with T(0, 0) = 1 and T(n, k) = 0 if n< < 0 or n< < k. (End)
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| EXAMPLE
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1, , 2;
1, , 4, , 5;
1, , 6, 14, 14;
1, , 8, 27, 48, 42;
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| STATUS
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approved
editing
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#51 by N. J. A. Sloane at Wed Apr 10 22:31:13 EDT 2019
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#50 by Jon E. Schoenfield at Sat Apr 06 22:48:53 EDT 2019
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Discussion
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| Tue Apr 09
| 17:16
| Ke Qiu: Does anybody know what still needs to be done with my comments? Thanks.
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#49 by Jon E. Schoenfield at Sat Apr 06 22:48:50 EDT 2019
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| EXAMPLE
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Triangle begins as:
1;
1, 2;
1, 4, 5;
1, 6, 14, 14;
1, 8, 27, 48, 42;
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| STATUS
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proposed
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#48 by Michel Marcus at Sat Apr 06 09:45:21 EDT 2019
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Discussion
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| Sat Apr 06
| 11:25
| Ke Qiu: Yes, Michel. Thank you so much.
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#47 by Michel Marcus at Sat Apr 06 09:45:16 EDT 2019
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| LINKS
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R. K. Guy, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/GUY/catwalks.html">Catwalks, sandsteps and Pascal pyramids</a>, J. Integer Sequences, Vol. 3 (2000), Article #00.1.6.
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| STATUS
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#46 by Michel Marcus at Sat Apr 06 03:35:03 EDT 2019
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