This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A287814 #10 May 22 2025 10:21:47
%S A287814 1,8,54,366,2482,16834,114178,774426,5252642,35626714,241642738,
%T A287814 1638972746,11116542082,75399367194,511405842898,3468675479466,
%U A287814 23526734684322,159573084361274,1082324835734258,7341006503296586,49791314679463362,337715954398900954
%N A287814 Number of octonary sequences of length n such that no two consecutive terms have distance 3.
%H A287814 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7, 0, -10).
%F A287814 For n>3, a(n) = 7*a(n-1) - 10*a(n-3), a(0)=1, a(1)=8, a(2)=54, a(3)=366.
%F A287814 G.f.: (1 + x - 2 x^2 - 2 x^3)/(1 - 7 x + 10 x^3).
%e A287814 For n=2 the a(2) = 64 - 10 = 54 sequences contain every combination except these ten: 03,30,14,41,25,52,36,63,47,74.
%t A287814 LinearRecurrence[{7, 0, -10}, {1, 8, 54, 366}, 40]
%o A287814 (Python)
%o A287814 def a(n):
%o A287814 if n in [0, 1, 2, 3]:
%o A287814 return [1, 8, 54, 366][n]
%o A287814 return 7*a(n-1)-10*a(n-3)
%Y A287814 Cf. A040000, A003945, A083318, A078057, A003946, A126358, A003946, A055099, A003947, A015448, A126473. A287804-A287819.
%K A287814 nonn,easy
%O A287814 0,2
%A A287814 _David Nacin_, Jun 02 2017