cp's OEIS Frontend

A277237 Number of strings of length n composed of symbols from the circular list [1,2,3,4,5,6] such that adjacent symbols in the string must be adjacent in the list. No runs of length 2 or more are allowed for symbols 1, 3 and 5.

%I A277237 #13 Oct 09 2016 15:59:23
%S A277237 1,6,15,39,99,255,651,1671,4275,10959,28059,71895,184131,471711,
%T A277237 1208235,3095079,7928019,20308335,52020411,133253751,341335395,
%U A277237 874350399,2239691979,5737093575,14695861491,37644235791,96427681755,247004624919,632715351939,1620733851615
%N A277237 Number of strings of length n composed of symbols from the circular list [1,2,3,4,5,6] such that adjacent symbols in the string must be adjacent in the list. No runs of length 2 or more are allowed for symbols 1, 3 and 5.
%H A277237 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1, 4).
%F A277237 G.f.: (1+5*x+5*x^2)/(1-x-4*x^2).
%F A277237 For n>=3, the recurrence is a(n) = a(n-1) + 4*a(n-2), a(1)=6, a(2)=15.
%F A277237 a(n) = 3*((13+3*sqrt(17))*z1^n-(13-3*sqrt(17))*z2^n)/(8*sqrt(17)), where z1=(1+sqrt(17))/2 and z2=(1-sqrt(17))/2.
%e A277237 For n=2 the 15 strings are: 12, 16, 21, 22, 23, 32, 34, 41, 43, 44, 54, 56, 61, 65, 66.
%e A277237 For n=3 the 39 strings are: 121, 122, 123, 161, 165, 166, 212, 216, 221, 222, 223, 232, 234, 321, 322, 323, 341, 343, 344, 412, 416, 432, 434, 441, 443, 444, 541, 543, 544, 561, 565, 566, 612, 616, 654, 656, 661, 665, 666.
%t A277237 CoefficientList[Series[(1 + 5 x + 5 x^2)/(1 - x - 4 x^2), {x, 0, 29}], x] (* _Michael De Vlieger_, Oct 07 2016 *)
%o A277237 (PARI) Vec((1+5*x+5*x^2)/(1-x-4*x^2) + O(x^40)) \\ _Michel Marcus_, Oct 06 2016
%Y A277237 Cf. A277236.
%K A277237 nonn,easy
%O A277237 0,2
%A A277237 _Stefan Hollos_, Oct 06 2016