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

0,2

Comments

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

Links

Table of n, a(n) for n=0..65.

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)

Example

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;
  ...

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

Crossrefs

Cf. A052940.

Sequence in context: A111003 A347904 A289277 * A340753 A239472 A234943

Adjacent sequences: A140179 A140180 A140181 * A140183 A140184 A140185

Keyword

nonn,tabl

Author

Gary W. Adamson, May 11 2008

Status

approved