The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A302180 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A302180

Number of 3D walks of type aad.
(history; published version)

#23 by Joerg Arndt at Tue Nov 05 05:41:18 EST 2024

STATUS

reviewed

approved

#22 by Alois P. Heinz at Tue Nov 05 05:24:26 EST 2024

STATUS

proposed

reviewed

#21 by Alois P. Heinz at Tue Nov 05 05:24:02 EST 2024

STATUS

editing

proposed

#20 by Alois P. Heinz at Tue Nov 05 05:23:17 EST 2024

DATA

1, 1, 3, 7, 23, 71, 251, 883, 3305, 12505, 48895, 193755, 783355, 3205931, 13302329, 55764413, 236174933, 1008773269, 4343533967, 18834033443, 82201462251, 360883031291, 1592993944723, 7066748314147, 31493800133173, 140953938878821, 633354801073571, 2856369029213263

MAPLE

A302180 := n-> add((-1)^(n-k)*binomial(n, k)*add(binomial(k, j)*M(j)*M(k-j), j=0..k), k=0..n): seq(A302180(n), n = 0 .. 26); # _Mélika Tebni, _, Nov 05 2024

KEYWORD

nonn,walk,more,changed

STATUS

proposed

editing

#19 by Mélika Tebni at Tue Nov 05 04:46:41 EST 2024

STATUS

editing

proposed

#18 by Mélika Tebni at Tue Nov 05 04:45:41 EST 2024

COMMENTS

Inverse binomial transform of A145867 (Number of 3D walks of type aae). - Mélika Tebni, Nov 05 2024

MAPLE

M := n-> add(binomial(n, 2*k)*binomial(2*k, k)/(k+1), k = 0 .. iquo(n, 2)): # Motzkin numbers

A302180 := n-> add((-1)^(n-k)*binomial(n, k)*add(binomial(k, j)*M(j)*M(k-j), j=0..k), k=0..n): seq(A302180(n), n = 0 .. 26); # Mélika Tebni, Nov 05 2024

STATUS

approved

editing

#17 by Michel Marcus at Sun Mar 07 03:07:24 EST 2021

STATUS

reviewed

approved

#16 by Joerg Arndt at Sun Mar 07 02:15:11 EST 2021

STATUS

proposed

reviewed

#15 by Jon E. Schoenfield at Sat Mar 06 11:00:25 EST 2021

STATUS

editing

proposed

#14 by Jon E. Schoenfield at Sat Mar 06 11:00:21 EST 2021

LINKS

Nachum Dershowitz, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL20/Dershowitz/dersh3.html">Touchard’'s Drunkard</a>, Journal of Integer Sequences, Vol. 20 (2017), #17.1.5.

STATUS

proposed

editing