cp's OEIS Frontend

A138056 Levels of substitution A103684 (based on the morphism f: 1->{1,2}, 2->{1,3}, 3->{3}) like Markov substitution taken as polynomials p(x,n)]and coefficients of the differential polynomials returned as q(x,n) =dp(x,n)dx coefficients (first zero omitted).

%I A138056 #7 Oct 26 2024 04:07:16
%S A138056 2,2,2,9,2,2,9,4,10,6,2,2,9,4,10,6,7,16,9,30,11,24,2,2,9,4,10,6,7,16,
%T A138056 9,30,11,24,13,28,15,48,17,36,19,20,42,22,69,2,2,9,4,10,6,7,16,9,30,
%U A138056 11,24,13,28,15,48,17,36,19,20,42,22,69,24,50,26,81,28,58,30,31,64,33,102,35
%N A138056 Levels of substitution A103684 (based on the morphism f: 1->{1,2}, 2->{1,3}, 3->{3}) like Markov substitution taken as polynomials p(x,n)]and coefficients of the differential polynomials returned as q(x,n) =dp(x,n)dx coefficients (first zero omitted).
%e A138056 {2},
%e A138056 {2, 2, 9},
%e A138056 {2, 2, 9, 4, 10, 6},
%e A138056 {2, 2, 9, 4, 10, 6, 7, 16, 9, 30, 11, 24},
%e A138056 {2, 2, 9, 4, 10, 6, 7, 16, 9, 30, 11, 24, 13, 28, 15, 48, 17, 36, 19, 20, 42, 22, 69},
%e A138056 {2, 2, 9, 4, 10, 6, 7, 16, 9, 30, 11, 24, 13, 28, 15, 48, 17, 36, 19, 20, 42, 22, 69, 24, 50, 26, 81, 28, 58, 30, 31, 64, 33, 102, 35, 72, 37, 76, 39, 120, 41, 84, 43}
%t A138056 s[1] = {1, 2}; s[2] = {1, 3}; s[3] = {1};
%t A138056 t[a_] := Flatten[s /@ a];
%t A138056 p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]];
%t A138056 (*A103684*);
%t A138056 a = Table[p[n], {n, 0, 10}];
%t A138056 Flatten[a];
%t A138056 b = Table[CoefficientList[D[Apply[Plus, Table[a[[n]][[m]]*x^( m - 1), {m, 1, Length[a[[n]]]}]], x], x], {n, 1, 11}];
%t A138056 Flatten[b]
%t A138056 Table[Apply[Plus, CoefficientList[D[Apply[Plus, Table[a[[n]][[m]]* x^(m - 1), {m, 1, Length[a[[n]]]}]], x], x]], {n, 1, 11}];
%Y A138056 Cf. A103684.
%K A138056 nonn,uned,less,tabf
%O A138056 1,1
%A A138056 _Roger L. Bagula_, May 02 2008