A138056 - OEIS

%I #7 Oct 26 2024 04:07:16

%S 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 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 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 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 {2},

%e {2, 2, 9},

%e {2, 2, 9, 4, 10, 6},

%e {2, 2, 9, 4, 10, 6, 7, 16, 9, 30, 11, 24},

%e {2, 2, 9, 4, 10, 6, 7, 16, 9, 30, 11, 24, 13, 28, 15, 48, 17, 36, 19, 20, 42, 22, 69},

%e {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 s[1] = {1, 2}; s[2] = {1, 3}; s[3] = {1};

%t t[a_] := Flatten[s /@ a];

%t p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]];

%t (*A103684*);

%t a = Table[p[n], {n, 0, 10}];

%t Flatten[a];

%t b = Table[CoefficientList[D[Apply[Plus, Table[a[[n]][[m]]*x^( m - 1), {m, 1, Length[a[[n]]]}]], x], x], {n, 1, 11}];

%t Flatten[b]

%t 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 Cf. A103684.

%K nonn,uned,less,tabf

%O 1,1

%A _Roger L. Bagula_, May 02 2008