A138056 - OEIS

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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).

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, 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, 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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..80.

EXAMPLE

{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, 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, 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}

MATHEMATICA

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

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

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

(*A103684*);

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

Flatten[a];

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

Flatten[b]

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

CROSSREFS

Cf. A103684.