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A253189
Triangle T(n, m)=Sum_{k=1..(n-m)/3} C(m, k)*T((n-m)/3, k), T(n,n)=1.
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
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
KEYWORD
nonn,tabl
AUTHOR
Vladimir Kruchinin, Mar 24 2015
STATUS
approved