OFFSET
0,4
COMMENTS
FORMULA
T(n, k) = 2*T(n-1, k) + T(n-1, k+1) for 0<k<n, with T(n, n)=T(n, 0)=T(n+1, n)=A002426(n), T(0, 0)=1, T(0, 1)=T(1, 0)=1.
EXAMPLE
Rows begin:
{1},
{1,1},
{3,1,3},
{7,5,3,7},
{19,13,13,7,19},
{51,39,33,33,19,51},
{141,111,99,85,89,51,141},
{393,321,283,259,229,243,141,393},
{1107,925,825,747,701,627,675,393,1107},
{3139,2675,2397,2195,2029,1929,1743,1893,1107,3139},
{8953,7747,6989,6419,5987,5601,5379,4893,5353,3139,8953},...
Convolution of each row with {1,2} forms the triangle:
{1,2},
{1,3,2},
{3,7,5,6},
{7,19,13,13,14},
{19,51,39,33,33,38},
{51,141,111,99,85,89,102},
{141,393,321,283,259,229,243,282},...
which, after the main diagonal is divided by 2 and the triangle is flattened, equals the original triangle in flattened form: {1,1,1,3,1,3,7,5,3,7,19,...}.
PROG
(PARI) T(n, k)=if(n<0 || k>n, 0, if(n==0 && k==0, 1, if(n==1 && k<=1, 1, if(k==n-1, T(n-1, 0), if(k==n, T(n, 0), 2*T(n-1, k)+T(n-1, k+1))))))
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Mar 04 2004
STATUS
approved