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

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.

Sequence in context: A298647 A068718 A075097 * A340080 A022459 A060804

Adjacent sequences: A138053 A138054 A138055 * A138057 A138058 A138059

Keyword

nonn,uned,less,tabf

Author

Roger L. Bagula, May 02 2008

Status

approved