cp's OEIS Frontend

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.

%I A208674 #18 Jun 13 2015 00:54:10
%S A208674 1,1,10,37,163,640,2503,9559,36154,135541,505279,1875592,6941035,
%T A208674 25629211,94478338,347857921,1279622611,4704064120,17284247263,
%U A208674 63484653151,233114307274,855817783741,3141437229271,11529935743528,42314502514051,155283277278547
%N 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.
%C A208674 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.
%H A208674 Alois P. Heinz, <a href="/A208674/b208674.txt">Table of n, a(n) for n = 0..500</a>
%H A208674 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-1,-14,-2,4)
%F A208674 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).
%e A208674 a(2) = 10 = |{aaabbb, aababb, aabbab, aabbba, abaabb, ababab, ababba, abbaab, abbaba, abbbaa}| with binary alphabet {a,b}.
%e A208674 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}.
%p A208674 a:= n-> (Matrix(5, (i, j)-> `if`(i=j-1, 1, `if`(i=5, [4, -2,
%p A208674         -14, -1, 5][j], 0)))^n. <<1, 1, 10, 37, 163>>)[1, 1]:
%p A208674 seq(a(n), n=0..30);
%Y A208674 Row n=3 of A208673.
%K A208674 nonn,walk,easy
%O A208674 0,3
%A A208674 _Alois P. Heinz_, Feb 29 2012