The On-Line Encyclopedia of Integer Sequences (OEIS)

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A247295

Number of weighted lattice paths B(n) having no uhd and no uHd strings.
(history; published version)

#13 by R. J. Mathar at Tue Jul 26 14:48:04 EDT 2022

STATUS

editing

approved

#12 by R. J. Mathar at Tue Jul 26 14:48:00 EDT 2022

FORMULA

D-finite with recurrence (n+3)*a(n) +(-2*n-3)*a(n-1) -n*a(n-2) +(-2*n+3)*a(n-3) +3*(n-3)*a(n-4) +4*(-n+6)*a(n-6) +(-2*n+15)*a(n-7) +(n-9)*a(n-8) +(2*n-21)*a(n-9) +(n-12)*a(n-10)=0. - R. J. Mathar, Jul 26 2022

STATUS

approved

editing

#11 by Bruno Berselli at Wed May 27 08:41:03 EDT 2015

STATUS

proposed

approved

#10 by Jean-François Alcover at Wed May 27 06:03:17 EDT 2015

STATUS

editing

proposed

#9 by Jean-François Alcover at Wed May 27 06:03:11 EDT 2015

MATHEMATICA

b[n_, y_, t_] := b[n, y, t] = If[y<0 || y>n || t == 3, 0, If[n == 0, 1, b[n-1, y-1, If[t == 2, 3, 0]] + b[n-1, y, If[t == 1, 2, 0]] + If[n>1, b[n-2, y, If[t == 1, 2, 0]] + b[n-2, y+1, 1], 0]]]; a[n_] := b[n, 0, 0]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, May 27 2015, after Alois P. Heinz *)

STATUS

approved

editing

#8 by Alois P. Heinz at Tue Sep 16 20:09:57 EDT 2014

STATUS

editing

approved

#7 by Alois P. Heinz at Tue Sep 16 20:09:38 EDT 2014

DATA

1, 1, 2, 4, 7, 14, 30, 64, 141, 316, 713, 1626, 3740, 8659, 20176, 47274, 111302, 263201, 624860, 1488736, 3558412, 8530533, 20505468, 49413242, 119347708, 288873639, 700582008, 1702190653, 4142880297, 10099352082, 24656876772, 60283224645, 147581756005

CROSSREFS

Cf. A004148, A247291, A247293, A247294.

#6 by Alois P. Heinz at Tue Sep 16 20:08:36 EDT 2014

LINKS

Alois P. Heinz, <a href="/A247295/b247295.txt">Table of n, a(n) for n = 0..1000</a>

MAPLE

# second Maple program:

b:= proc(n, y, t) option remember; `if`(y<0 or y>n or t=3, 0,

`if`(n=0, 1, b(n-1, y-1, `if`(t=2, 3, 0))+b(n-1, y,

`if`(t=1, 2, 0))+`if`(n>1, b(n-2, y, `if`(t=1, 2, 0))+

b(n-2, y+1, 1), 0)))

end:

a:= n-> b(n, 0$2):

seq(a(n), n=0..40); # Alois P. Heinz, Sep 16 2014

STATUS

proposed

editing

#5 by Emeric Deutsch at Tue Sep 16 20:00:22 EDT 2014

STATUS

editing

proposed

#4 by Emeric Deutsch at Tue Sep 16 20:00:16 EDT 2014

NAME

Number of weighted lattice paths B(n) having no uhd and no uHd stepsstrings.

STATUS

proposed

editing