A140182 Binomial transform of an infinite bidiagonal matrix with (1,3,1,3,1,3,...) in the main diagonal, (1,1,1,...) in the subdiagonal, the rest zeros.

1, 2, 3, 3, 7, 1, 4, 12, 4, 3, 5, 18, 10, 13, 1, 6, 25, 20, 35, 6, 3, 7, 33, 35, 75, 21, 19, 1, 8, 42, 56, 140, 56, 70, 8, 3, 9, 52, 84, 238, 126, 196, 36, 25, 1, 10, 63, 120, 378, 252, 462, 120, 117, 10, 3, 11, 75, 165, 570, 462, 966, 330, 405, 55, 31, 1

Offset: 0

Author

Gary W. Adamson, May 11 2008

Keywords

• nonn
• tabl

Comments

Row sums = A052940: (1, 5, 11, 23, 47, 95, ...).

Examples

			First few rows of the triangle are:
  1;
  2,  3;
  3,  7,  1;
  4, 12,  4,  3;
  5, 18, 10, 13,  1;
  6, 25, 20, 35,  6,  3;
  7, 33, 35, 75, 21, 19,  1;
  ...
		

Crossrefs

Cf. A052940.

Programs

Maple

T:=proc(n,k) if `mod`(k,2)=0 then binomial(n+1,k+1) else 2*binomial(n,k)+binomial(n+1,k+1) end if end proc: for n from 0 to 10 do seq(T(n,k),k=0..n) end do; # yields sequence in triangular form - Emeric Deutsch, May 18 2008

Formula

A007318 as an infinite lower triangular matrix * a bidiagonal matrix with (1,3,1,3,1,3,...) in the main diagonal, (1,1,1,...) in the subdiagonal and the rest zeros.

From Emeric Deutsch, May 18 2008: (Start)

T(n, 2k) = binomial(n+1, 2k+1);

T(n, 2k+1) = 2*binomial(n, 2k+1) + binomial(n+1, 2k+2). (End)