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A284840 Number of quinternary strings avoiding consecutive digits i,i+1 and i,i+2.

%I A284840 #6 Apr 03 2017 16:48:19
%S A284840 1,5,18,63,224,799,2846,10132,36073,128438,457304,1628224,5797263,
%T A284840 20641062,73492179,261667749,931663897,3317174627,11810748015,
%U A284840 42051982296,149725420655,533095002085,1898076358760,6758070980980,24062005289281,85672390859855
%N A284840 Number of quinternary strings avoiding consecutive digits i,i+1 and i,i+2.
%H A284840 Alois P. Heinz, <a href="/A284840/b284840.txt">Table of n, a(n) for n = 0..1000</a>
%H A284840 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-7,8,-5,1).
%F A284840 G.f.: -1/(x^5-5*x^4+8*x^3-7*x^2+5*x-1).
%e A284840 a(2) = 18: 00, 03, 04, 10, 11, 14, 20, 21, 22, 30, 31, 32, 33, 40, 41, 42, 43, 44.
%p A284840 a:= n->(<<0|1|0|0|0>, <0|0|1|0|0>, <0|0|0|1|0>,
%p A284840          <0|0|0|0|1>, <1|-5|8|-7|5>>^n)[5$2]:
%p A284840 seq(a(n), n=0..30);
%Y A284840 Cf. A277668.
%K A284840 nonn,easy
%O A284840 0,2
%A A284840 _Alois P. Heinz_, Apr 03 2017