cp's OEIS Frontend

A187185 Parse the infinite string 0123456012345601234560... into distinct phrases 0, 1, 2, 3, 4, 5, 6, 01, 23, 45, 60, 12, 34, 56, 012, ...; a(n) = length of n-th phrase.

%I A187185 #12 Jan 31 2020 16:06:32
%S A187185 1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,
%T A187185 5,6,6,6,6,6,6,6,7,8,7,8,7,8,7,8,7,8,7,8,7,8,9,9,9,9,9,9,9,10,10,10,
%U A187185 10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,13,13,13,13,13,13,13,14,15,14,15,14,15,14,15,14,15,14,15,14,15,16,16,16,16,16,16,16,17,17,17,17,17,17,17,18
%N A187185 Parse the infinite string 0123456012345601234560... into distinct phrases 0, 1, 2, 3, 4, 5, 6, 01, 23, 45, 60, 12, 34, 56, 012, ...; a(n) = length of n-th phrase.
%C A187185 See A187180 for details.
%H A187185 Ray Chandler, <a href="/A187185/b187185.txt">Table of n, a(n) for n = 1..1000</a>
%H A187185 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).
%F A187185 After the initial block of seven 1's, the sequence is quasi-periodic with period 49, increasing by 7 after each block.
%F A187185 From _Colin Barker_, Jan 31 2020: (Start)
%F A187185 G.f.: x*(1 + x^7 + x^14 + x^21 + x^28 + x^35 + x^42 + x^43 - x^44 + x^45 - x^46 + x^47 - x^48 - x^50 + x^51 - x^52 + x^53 - x^54 + x^55) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)*(1 + x^7 + x^14 + x^21 + x^28 + x^35 + x^42)).
%F A187185 a(n) = a(n-1) + a(n-49) - a(n-50) for n>56.
%F A187185 (End)
%t A187185 Join[{1, 1, 1, 1, 1, 1},LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1},{1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8},114]] (* _Ray Chandler_, Aug 26 2015 *)
%o A187185 (PARI) Vec(x*(1 + x^7 + x^14 + x^21 + x^28 + x^35 + x^42 + x^43 - x^44 + x^45 - x^46 + x^47 - x^48 - x^50 + x^51 - x^52 + x^53 - x^54 + x^55) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)*(1 + x^7 + x^14 + x^21 + x^28 + x^35 + x^42)) + O(x^80)) \\ _Colin Barker_, Jan 31 2020
%Y A187185 See A187180-A187188 for alphabets of size 2 through 10.
%K A187185 nonn,easy
%O A187185 1,8
%A A187185 _N. J. A. Sloane_, Mar 06 2011