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A208674 Number of words, either empty or beginning with the first letter of the n-ary alphabet, where each letter of the alphabet occurs 3 times and letters of neighboring word positions are equal or neighbors in the alphabet. 2
1, 1, 10, 37, 163, 640, 2503, 9559, 36154, 135541, 505279, 1875592, 6941035, 25629211, 94478338, 347857921, 1279622611, 4704064120, 17284247263, 63484653151, 233114307274, 855817783741, 3141437229271, 11529935743528, 42314502514051, 155283277278547 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also the number of (3*n-1)-step walks on n-dimensional cubic lattice from (1,0,...,0) to (3,3,...,3) with positive unit steps in all dimensions such that the absolute difference of the dimension indices used in consecutive steps is <= 1.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (5,-1,-14,-2,4)

FORMULA

G.f.: -(4*x^4+2*x^3+6*x^2-4*x+1) / (4*x^5-2*x^4-14*x^3-x^2+5*x-1).

EXAMPLE

a(2) = 10 = |{aaabbb, aababb, aabbab, aabbba, abaabb, ababab, ababba, abbaab, abbaba, abbbaa}| with binary alphabet {a,b}.

a(3) = 37 = |{aaabbbccc, aaabbcbcc, aaabbccbc, aaabbcccb, aaabcbbcc, aaabcbcbc, aaabcbccb, aaabccbbc, aaabccbcb, aaabcccbb, aababbccc, aababcbcc, aababccbc, aababcccb, aabbabccc, aabbcccba, aabcbabcc, aabcbccba, aabccbabc, aabccbcba, aabcccbab, aabcccbba, abaabbccc, abaabcbcc, abaabccbc, abaabcccb, abababccc, ababcccba, abbaabccc, abbcccbaa, abcbaabcc, abcbccbaa, abccbaabc, abccbcbaa, abcccbaab, abcccbaba, abcccbbaa}| with ternary alphabet {a,b,c}.

MAPLE

a:= n-> (Matrix(5, (i, j)-> `if`(i=j-1, 1, `if`(i=5, [4, -2,

        -14, -1, 5][j], 0)))^n. <<1, 1, 10, 37, 163>>)[1, 1]:

seq(a(n), n=0..30);

CROSSREFS

Row n=3 of A208673.

Sequence in context: A116970 A199208 A110528 * A137280 A071261 A129426

Adjacent sequences:  A208671 A208672 A208673 * A208675 A208676 A208677

KEYWORD

nonn,walk,easy

AUTHOR

Alois P. Heinz, Feb 29 2012

STATUS

approved

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Last modified November 24 07:33 EST 2020. Contains 338607 sequences. (Running on oeis4.)