OFFSET
0,2
COMMENTS
Row sums = A052940: (1, 5, 11, 23, 47, 95, ...).
FORMULA
A007318 as an infinite lower triangular matrix * a bidiagonal matrix with (1,3,1,3,1,3,...) in the main diagonal, (1,1,1,...) in the subdiagonal and the rest zeros.
From Emeric Deutsch, May 18 2008: (Start)
T(n, 2k) = binomial(n+1, 2k+1);
T(n, 2k+1) = 2*binomial(n, 2k+1) + binomial(n+1, 2k+2). (End)
EXAMPLE
First few rows of the triangle are:
1;
2, 3;
3, 7, 1;
4, 12, 4, 3;
5, 18, 10, 13, 1;
6, 25, 20, 35, 6, 3;
7, 33, 35, 75, 21, 19, 1;
...
MAPLE
T:=proc(n, k) if `mod`(k, 2)=0 then binomial(n+1, k+1) else 2*binomial(n, k)+binomial(n+1, k+1) end if end proc: for n from 0 to 10 do seq(T(n, k), k=0..n) end do; # yields sequence in triangular form - Emeric Deutsch, May 18 2008
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, May 11 2008
STATUS
approved