A160019 Triangle: Lodumo_2 applied to each row of Pascal's triangle .

1, 1, 3, 1, 0, 3, 1, 3, 5, 7, 1, 0, 2, 4, 3, 1, 3, 0, 2, 5, 7, 1, 0, 3, 2, 5, 4, 7, 1, 3, 5, 7, 9, 11, 13, 15, 1, 0, 2, 4, 6, 8, 10, 12, 3, 1, 3, 0, 2, 4, 6, 8, 10, 5, 7, 1, 0, 3, 2, 4, 6, 8, 10, 5, 12, 7, 1, 3, 5, 7, 0, 2, 4, 6, 9, 11, 13, 15, 1, 0, 2, 4, 3, 6, 8, 10, 5, 12, 14, 16, 7

Offset: 0

Author

Philippe Deléham, Apr 29 2009, May 02 2009

Keywords

• easy
• nonn
• tabl

Examples

			Triangle begins:
  1;
  1, 3;
  1, 0, 3;
  1, 3, 5, 7;
  1, 0, 2, 4, 3;
  1, 3, 0, 2, 5, 7; ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1325
• OEIS wiki, Lodumo transform

Crossrefs

Row sums are A160020.

Cf. A007318, A047999, A261363.

Programs

PARI

\\ here S(n,k) is A047999.
S(n,k)={bitand(n-k, k)==0}
row(n)={my(v=vector(n+1), b=0); for(k=0, n, if(S(n,k), b++; v[1+k]=2*b-1, v[1+k]=2*(k-b))); v}
{ for(n=0, 10, print(row(n))) } \\ Andrew Howroyd, Feb 02 2020

Formula

T(n,0)=A000012(n)=1; T(n,1)=A010674(n). - Philippe Deléham, Nov 15 2011