OFFSET
0,2
COMMENTS
Row sums of A114213.
LINKS
Jeffrey Shallit and Lukas Spiegelhofer, Continuants, run lengths, and Barry's modified Pascal triangle, arXiv:1710.06203 [math.CO], 2017.
FORMULA
EXAMPLE
From Omar E. Pol, Jun 09 2009: (Start)
Triangle begins:
1;
2,3;
4,4,4,6;
8,6,4,6,8,8,8,12;
16,10,4,6,8,8,8,12,16,12,8,12,16,16,16,24;
32,18,4,6,8,8,8,12,16,12,8,12,16,16,16,24,32,20,8,12,16,16,16,24,32,24,...
Also, we can write the initial term followed by a triangle:
1;
2;
3,4;
4,4,6,8;
6,4,6,8,8,8,12,16;
10,4,6,8,8,8,12,16,12,8,12,16,16,16,24,32;
18,4,6,8,8,8,12,16,12,8,12,16,16,16,24,32,20,8,12,16,16,16,24,32,24,16,...
Also, we can write first two terms followed by a triangle:
1;
2;
3;
4,4;
4,6,8,6;
4,6,8,8,8,12,16,10;
4,6,8,8,8,12,16,12,8,12,16,16,16,24,32,18;
4,6,8,8,8,12,16,12,8,12,16,16,16,24,32,20,8,12,16,16,16,24,32,24,16,24,32,...
(End)
PROG
(PARI) T(n, k) = sum(j=0, n-k, binomial(k, j)*binomial(n-k, j)*(1+(-1)^j)/2) % 2; \\ A114213
a(n) = sum(k=0, n-1, T(n, k)); \\ Michel Marcus, Jun 06 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Nov 17 2005
STATUS
approved