A253189 Triangle T(n, m)=Sum_{k=1..(n-m)/3} C(m, k)*T((n-m)/3, k), T(n,n)=1.

1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 3, 0, 0, 1, 0, 0, 0, 4, 0, 0, 1, 0, 1, 0, 0, 5, 0, 0, 1, 0, 0, 3, 0, 0, 6, 0, 0, 1, 0, 0, 0, 6, 0, 0, 7, 0, 0, 1, 0, 0, 0, 0, 10, 0, 0, 8, 0, 0, 1, 0, 0, 1, 0, 0, 15, 0, 0, 9, 0, 0, 1, 1, 0, 0, 4, 0, 0, 21, 0, 0, 10, 0, 0, 1, 0, 2, 0, 0, 10, 0, 0, 28, 0, 0, 11, 0, 0, 1, 0, 0, 3, 0, 0, 20, 0, 0, 36, 0, 0, 12, 0, 0, 1

Offset

1,12

Links

Table of n, a(n) for n=1..120.

Milan Janjic, Binomial Coefficients and Enumeration of Restricted Words, Journal of Integer Sequences, 2016, Vol 19, #16.7.3

Formula

G.f.: A(x)^m=Sum_{n>=m} T(n,m)*x^n, where A(x)=Sum_{n>0} x^((3^n-1)/2).

Example

1;
0, 1;
0, 0, 1;
1, 0, 0, 1;
0, 2, 0, 0, 1;
0, 0, 3, 0, 0, 1;

Prog

(Maxima)
T(n, m):=if n=m then 1 else sum(binomial(m, k)*T((n-m)/3, k), k, 1, (n-m)/3);

Crossrefs

Cf. A003462, A113047, A253184, A253190.

Sequence in context: A188170 A363805 A212193 * A126030 A111373 A336757

Adjacent sequences: A253186 A253187 A253188 * A253190 A253191 A253192

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Mar 24 2015

Status

approved