

A182412


Triangle T(n,k), read by rows, given by (1, 2, 2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 2, 1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.


0



1, 1, 1, 3, 6, 3, 5, 17, 19, 7, 11, 48, 80, 60, 17, 21, 119, 270, 308, 177, 41, 43, 290, 823, 1256, 1087, 506, 99, 85, 677, 2321, 4447, 5147, 3601, 1411, 239, 171, 1556, 6234, 14360, 20806, 19424, 11416, 3864, 577
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,4


COMMENTS



LINKS



FORMULA

G.f.: (1y*x)/(1(1+2*y)*x(2+3*y+y^2)*x^2)
T(n,k) = T(n1,k) + 2*T(n1,k1) + 2*T(n2,k) + 3*T(n2,k1) + T(n2,k2), T(0,0) = T(1,0) = T(1,1) = 1, T(2,0) = T(2,2) = 3, T(2,1) = 6 and T(n,k) = 0 if k<0 or if k>n.
Sum_{k, 0<=k<=n} T(n,k)*(1)^k = A000007(n).


EXAMPLE

Triangle begins
1
1, 1
3, 6, 3
5, 17, 19, 7
11, 48, 80, 60, 17
21, 119, 270, 308, 177, 41
43, 290, 823, 1256, 1087, 506, 99
85, 677, 2321, 4447, 5147, 3601, 1411, 239


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



