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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
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 (list; table; graph; refs; listen; history; text; internal format)
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: A100228 A111003 A289277 * A239472 A234943 A209494

Adjacent sequences:  A140179 A140180 A140181 * A140183 A140184 A140185

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, May 11 2008

STATUS

approved

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Last modified November 21 06:00 EST 2019. Contains 329350 sequences. (Running on oeis4.)