The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A276903 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A276903

Number of positive walks with n steps {-2,-1,0,1,2} starting at the origin, ending at altitude 2, and staying strictly above the x-axis.
(history; published version)

#22 by Alois P. Heinz at Tue Oct 11 08:42:00 EDT 2016

STATUS

editing

approved

#21 by Alois P. Heinz at Tue Oct 11 08:41:55 EDT 2016

LINKS

Alois P. Heinz, <a href="/A276903/b276903.txt">Table of n, a(n) for n = 0..1437</a>

#20 by Alois P. Heinz at Tue Oct 11 08:38:56 EDT 2016

DATA

0, 1, 2, 7, 25, 96, 382, 1567, 6575, 28096, 121847, 534953, 2373032, 10619922, 47890013, 217395690, 992640367, 4555957948, 21007405327, 97266928685, 452046424465, 2108022305795, 9860773604035, 46256877824220, 217555982625385, 1025667805621986, 4846240583558277

KEYWORD

nonn,more,walk,changed

STATUS

proposed

editing

#19 by Davin Park at Mon Oct 10 21:13:17 EDT 2016

STATUS

editing

proposed

#18 by Davin Park at Mon Oct 10 21:11:20 EDT 2016

MATHEMATICA

A276903[n_] := (Do[walks[m, k, 2], {m, n}, {k, 2 m}]; walks[n, 2, 2]; ) (* Davin Park, Oct 10 2016 *)

STATUS

proposed

editing

#17 by Davin Park at Mon Oct 10 19:19:40 EDT 2016

STATUS

editing

proposed

#16 by Davin Park at Mon Oct 10 19:19:33 EDT 2016

MATHEMATICA

dpwalks[n_, k_, h_] = 0;

dpwalks[1, k_, h_] := Boole[0 < k <= h];

dpwalks[n_, k_, h_] /; n >= 2 && k > 0 := dpwalks[n, k, h] = Sum[dpwalks[n - 1, k + x, h], {x, -h, h}];

(* walks represents the number of positive walks with n steps {-h, -h+1, ... , h} that end at altitude k *)

A276903[n_] := dpwalks[n, 2, 2]; (* Davin Park, Oct 10 2016 *)

#15 by Alonso del Arte at Mon Oct 10 15:41:27 EDT 2016

STATUS

proposed

editing

#14 by Davin Park at Mon Oct 10 15:32:37 EDT 2016

STATUS

editing

proposed

Discussion

Mon Oct 10

15:41

Alonso del Arte: What's "dp"? Different parks? Deviation parameters? It needs a more meaningful name so that it's easier to understand how this 3-parameter function can be used in other contexts.

#13 by Davin Park at Mon Oct 10 15:30:23 EDT 2016

MATHEMATICA

dp[n_, k_, h_] = 0;

dp[1, k_, h_] := Boole[0 < k <= h];

dp[n_, k_, h_] /; n >= 2 && k > 0 := dp[n, k, h] = Sum[dp[n - 1, k + x, h], {x, -h, h}];

A276903[n_] := dp[n, 2, 2]; (* Davin Park, Oct 10 2016 *)

STATUS

approved

editing