Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #22 Aug 24 2017 16:36:08
%S 1,36,1297,46729,1683577,60656797,2185374961,78735837637,
%T 2836736138665,102203420474269,3682238546710945,132665625592223221,
%U 4779746882367738841,172207232713967895181,6204372685172893559377,223534399861459456068709
%N Numbers of words on {0,1,...,36} having no isolated zeros.
%C 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 Colin Barker, <a href="/A255821/b255821.txt">Table of n, a(n) for n = 0..642</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (37,-36,36).
%F G.f.: -(x^2 - x + 1)/(36*x^3 - 36*x^2 + 37*x - 1). - _Colin Barker_, Mar 09 2015
%F a(n) = 37*a(n-1) - 36*a(n-2) + 36*a(n-3). - _G. C. Greubel_, Jun 02 2016
%t 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 LinearRecurrence[{37,-36,36}, {1, 36, 1297}, 100] (* _G. C. Greubel_, Jun 02 2016 *)
%o (PARI) Vec(-(x^2-x+1)/(36*x^3-36*x^2+37*x-1) + O(x^100)) \\ _Colin Barker_, Mar 09 2015
%Y Cf. A255116, A255118, A254658, A254660, A255633, A255630.
%K nonn,easy
%O 0,2
%A _Milan Janjic_, Mar 07 2015