OFFSET
0,2
COMMENTS
FORMULA
T(n, [n/2]) = 2^n. T(n+1, 0) = 2*T(n, n) (n>=0); T(0, 0)=1; T(n, k) = T(n, k-1) XOR T(n-1, k-1) for n>k>0. T(n, k) = SumXOR_{i=0..k} (C(k, i)mod 2)*T(n-i, 0), where SumXOR is the analog of summation under the binary XOR operation and C(k, i)mod 2 = A047999(k, i).
EXAMPLE
Rows begin:
[_1],
[_2,3],
[6,_4,7],
[14,_8,12,11],
[22,24,_16,28,23],
[46,56,_32,48,44,59],
[118,88,96,_64,112,92,103],
[206,184,224,_128,192,176,236,139],
[278,472,352,384,_256,448,368,412,279],
[558,824,736,896,_512,768,704,944,556,827],
[1654,1112,1888,1408,1536,_1024,1792,1472,1648,1116,1895],...
notice that the column terms equal twice the diagonal (with offset), and that the central terms in the rows form the powers of 2.
PROG
(PARI) T(n, k)=if(n<k || k<0, 0, if(k==0, if(n==0, 1, 2*T(n-1, n-1)), bitxor(T(n, k-1), T(n-1, k-1))); )
CROSSREFS
KEYWORD
AUTHOR
Paul D. Hanna, Oct 29 2004
STATUS
approved