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.

A255115 Number of n-length words on {0,1,2} in which 0 appears only in runs of length 2.

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%I A255115 #26 Oct 13 2022 02:49:38
%S A255115 1,2,5,12,28,66,156,368,868,2048,4832,11400,26896,63456,149712,353216,
%T A255115 833344,1966112,4638656,10944000,25820224,60917760,143723520,
%U A255115 339087488,800010496,1887468032,4453111040,10506243072,24787422208,58481066496,137974619136
%N A255115 Number of n-length words on {0,1,2} in which 0 appears only in runs of length 2.
%C A255115 Apparently a(n) = A239333(n).
%H A255115 Colin Barker, <a href="/A255115/b255115.txt">Table of n, a(n) for n = 0..1000</a>
%H A255115 D. Birmajer, J. B. Gil, and M. D. Weiner, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Gil/gil6.html">On the Enumeration of Restricted Words over a Finite Alphabet</a>, J. Int. Seq. 19 (2016) # 16.1.3, example 10.
%H A255115 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,2).
%F A255115 a(n+3) = 2*a(n+2) + 2*a(n) with n>1, a(0) = 1, a(1) = 2, a(2)=5.
%F A255115 G.f.: -(x^2+1) / (2*x^3+2*x-1). - _Colin Barker_, Feb 15 2015
%F A255115 a(n) = A052912(n)+A052912(n-2). - _R. J. Mathar_, Jun 18 2015
%t A255115 RecurrenceTable[{a[0] == 1, a[1] == 2,  a[2]== 5, a[n] == 2 a[n - 1] + 2 a[n - 3]}, a[n], {n, 0, 29}]
%o A255115 (PARI) Vec(-(x^2+1)/(2*x^3+2*x-1) + O(x^100)) \\ _Colin Barker_, Feb 15 2015
%Y A255115 Cf. A000930, A239333, A239340, A254657, A254600, A254664.
%K A255115 nonn,easy
%O A255115 0,2
%A A255115 _Milan Janjic_, Feb 14 2015