A059782 Triangle T(n,k) giving exponent of power of 3 dividing entry (n,k) of trinomial triangle A027907.

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 2, 1, 1, 0, 0, 0, 1, 1, 0, 2, 2, 1, 2, 2, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 1, 2, 2, 1, 2, 2, 0, 2, 2, 1, 2, 2, 1, 2, 2, 0, 0, 0, 0, 1, 1

Offset: 0

Author

N. J. A. Sloane, Feb 22 2001

Keywords

• nonn
• easy
• tabf

Examples

			0; 0,0,0; 0,0,1,0,0; 0,1,1,0,1,1,0; ...
		

References

• Boris A. Bondarenko, Generalized Pascal Triangles and Pyramids (in Russian), FAN, Tashkent, 1990, ISBN 5-648-00738-8.

Links

• Boris A. Bondarenko, Generalized Pascal Triangles and Pyramids, English translation published by Fibonacci Association, Santa Clara Univ., Santa Clara, CA, 1993; see p. 118.

Programs

Maple

with(numtheory): T := proc(i,j) option remember: if i >= 0 and j=0 then RETURN(1) fi: if i >= 0 and j=2*i then RETURN(1) fi: if i >= 1 and j=1 then RETURN(i) fi: if i >= 1 and j=2*i-1 then RETURN(i) fi: T(i-1,j-2)+T(i-1,j-1)+T(i-1,j): end: for i from 0 to 20 do for j from 0 to 2*i do if T(i,j) mod 3 <> 0 then printf(`%d,`,0) fi: if T(i,j) mod 3 = 0 and T(i,j) mod 2 = 0 then printf(`%d,`, ifactors(T(i,j))[2,2,2] ) fi: if T(i,j) mod 3 = 0 and T(i,j) mod 2 = 1 then printf(`%d,`, ifactors(T(i,j))[2,1,2] ) fi: #printf(`%d,`,T(i,j)) od:od: # James Sellers, Feb 22 2001

Extensions

More terms from James Sellers, Feb 22 2001