The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A247507

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A247507

Square array read by ascending antidiagonals, n>=0, k>=0. Row n is the expansion of (1-n*x-sqrt(n^2*x^2-2*n*x-4*x+1))/(2*x).
(history; published version)

#14 by R. J. Mathar at Fri Jun 25 05:51:00 EDT 2021

STATUS

editing

approved

#13 by R. J. Mathar at Fri Jun 25 05:49:20 EDT 2021

LINKS

L. Yang, S.-L. Yang, <a href="https://doi.org/10.1007/s00373-020-02185-6">A relation between Schroder paths and Motzkin paths</a>, Graphs Combinat. 36 (2020) 1489-1502, eq. (5).

STATUS

approved

editing

#12 by Susanna Cuyler at Fri Apr 06 17:28:23 EDT 2018

STATUS

proposed

approved

#11 by Ilya Gutkovskiy at Fri Apr 06 13:03:13 EDT 2018

STATUS

editing

proposed

#10 by Ilya Gutkovskiy at Fri Apr 06 08:47:54 EDT 2018

FORMULA

G.f. of row n: 1/(1 - n*x - x/(1 - n*x - x/(1 - n*x - x/(1 - n*x - x/(1 - ...))))), a continued fraction. - Ilya Gutkovskiy, Apr 06 2018

CROSSREFS

Main diagonal gives A302286.

STATUS

approved

editing

#9 by Alois P. Heinz at Thu May 28 08:32:40 EDT 2015

STATUS

editing

approved

#8 by Alois P. Heinz at Thu May 28 08:31:30 EDT 2015

OFFSET

1,0,5

MAPLE

for n from 1 0 to 10 do lprint(PolynomialTools:-CoefficientList( convert(series(gf(n), x, 8), polynom), x)) od;

EXTENSIONS

Offset changed to 0 by Alois P. Heinz, May 28 2015

STATUS

approved

editing

Discussion

Thu May 28

08:32

Alois P. Heinz: Name has n>=0, example has row 0, so offset has to be 0.

#7 by Michel Marcus at Mon Dec 01 03:37:47 EST 2014

STATUS

reviewed

approved

#6 by Joerg Arndt at Mon Dec 01 02:54:54 EST 2014

STATUS

proposed

reviewed

#5 by Peter Luschny at Mon Dec 01 02:48:11 EST 2014

STATUS

editing

proposed

Discussion

Mon Dec 01

02:54

Joerg Arndt: Nice one!