cp's OEIS Frontend

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.

A255821 Numbers of words on {0,1,...,36} having no isolated zeros.

This page as a plain text file.
%I A255821 #22 Aug 24 2017 16:36:08
%S A255821 1,36,1297,46729,1683577,60656797,2185374961,78735837637,
%T A255821 2836736138665,102203420474269,3682238546710945,132665625592223221,
%U A255821 4779746882367738841,172207232713967895181,6204372685172893559377,223534399861459456068709
%N A255821 Numbers of words on {0,1,...,36} having no isolated zeros.
%C A255821 The number p_n = a(n)/37^n equals the probability that in n trials in single zero (European) Roulette zero will not appear isolated. For example, p_10 is approximately 0.021.
%H A255821 Colin Barker, <a href="/A255821/b255821.txt">Table of n, a(n) for n = 0..642</a>
%H A255821 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (37,-36,36).
%F A255821 G.f.: -(x^2 - x + 1)/(36*x^3 - 36*x^2 + 37*x - 1). - _Colin Barker_, Mar 09 2015
%F A255821 a(n) = 37*a(n-1) - 36*a(n-2) + 36*a(n-3). - _G. C. Greubel_, Jun 02 2016
%t A255821 RecurrenceTable[{a[0] == 1, a[1] == 36,  a[2]== 1297, a[n] == 37 a[n - 1] - 36 a[n - 2] + 36 a[n - 3]}, a[n], {n, 0, 15}]
%t A255821 LinearRecurrence[{37,-36,36}, {1, 36, 1297}, 100] (* _G. C. Greubel_, Jun 02 2016 *)
%o A255821 (PARI) Vec(-(x^2-x+1)/(36*x^3-36*x^2+37*x-1) + O(x^100)) \\ _Colin Barker_, Mar 09 2015
%Y A255821 Cf. A255116, A255118, A254658, A254660, A255633, A255630.
%K A255821 nonn,easy
%O A255821 0,2
%A A255821 _Milan Janjic_, Mar 07 2015