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A153361 Number of zig-zag paths from top to bottom of a rectangle of width 12 with n rows. 0
12, 22, 42, 80, 154, 296, 572, 1104, 2138, 4136, 8020, 15536, 30148, 58450, 113472, 220110, 427410, 829352, 1610628, 3125954, 6071028, 11784514, 22887536, 44431506, 86293452, 167532792, 325373382, 631721620, 1226878704, 2382108386 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Number of words of length n using a 12 symbol alphabet where neighboring letters are neighbors in the alphabet. - Andrew Howroyd, Apr 17 2017

LINKS

Table of n, a(n) for n=1..30.

Joseph Myers, BMO 2008--2009 Round 1 Problem 1---Generalisation

Index entries for linear recurrences with constant coefficients, signature (1,5,-4,-6,3,1).

FORMULA

G.f.: -2*x*(3*x^5 +12*x^4 -12*x^3 -20*x^2 +5*x +6)/(x^6 +3*x^5 -6*x^4 -4*x^3 +5*x^2 +x -1). [Colin Barker, Sep 02 2012]

MATHEMATICA

b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i == 0, Sum[b[n - 1, j, k], {j, 1, k}], If[i > 1, b[n - 1, i - 1, k], 0] + If[i < k, b[n - 1, i + 1, k], 0]]]; a[n_] := b[n, 0, 12]; Array[a, 30] (* Jean-Fran├žois Alcover, Oct 10 2017, after Alois P. Heinz *)

CROSSREFS

Column 12 of A220062.

Twice A129638.

Sequence in context: A124885 A115745 A129639 * A200197 A115709 A115703

Adjacent sequences:  A153358 A153359 A153360 * A153362 A153363 A153364

KEYWORD

easy,nonn

AUTHOR

Joseph Myers, Dec 24 2008

STATUS

approved

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Last modified October 1 22:45 EDT 2022. Contains 357173 sequences. (Running on oeis4.)