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 A287833 #16 May 22 2025 10:21:46
%S A287833 1,11,103,967,9079,85243,800351,7514541,70554457,662439857,6219685951,
%T A287833 58396989455,548292695881,5147951686649,48334414751849,
%U A287833 453814602701801,4260891430727991,40005754941255473,375616336261903907,3526683405274793053,33112233522155404139
%N A287833 Number of words of length n over the alphabet {0,1,...,10} such that no two consecutive terms have distance 2.
%H A287833 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (10,-2,-37,16,19,1).
%F A287833 a(n) = 10*a(n-1) - 2*a(n-2) - 37*a(n-3) + 16*a(n-4) + 19*a(n-5) + a(n-6), a(0)=1, a(1)=11, a(2)=103, a(3)=967, a(4)=9079, a(5)=85243.
%F A287833 G.f.: (-1 - x + 5*x^2 + 4*x^3 - 6*x^4 - 3*x^5)/(-1 + 10*x - 2*x^2 - 37*x^3 + 16*x^4 + 19*x^5 + x^6).
%t A287833 LinearRecurrence[{10, -2, -37, 16, 19, 1}, {1, 11, 103, 967, 9079, 85243}, 20]
%o A287833 (Python)
%o A287833 def a(n):
%o A287833 if n in [0,1,2,3,4,5]:
%o A287833 return [1, 11, 103, 967, 9079, 85243][n]
%o A287833 return 10*a(n-1) - 2*a(n-2) - 37*a(n-3) + 16*a(n-4) + 19*a(n-5) + a(n-6)
%Y A287833 Cf. A040000, A003945, A083318, A078057, A003946, A126358, A003946, A055099, A003947, A015448, A126473. A287804-A287819. A287825-A287839.
%K A287833 nonn,easy
%O A287833 0,2
%A A287833 _David Nacin_, Jun 07 2017