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A124732 Triangle P*M, where P is the Pascal triangle written as an infinite lower triangular matrix and M is the infinite bidiagonal matrix with (1,2,1,2,...) in the main diagonal and (2,1,2,1,...) in the subdiagonal. 2
1, 3, 2, 5, 5, 1, 7, 9, 5, 2, 9, 14, 14, 9, 1, 11, 20, 30, 25, 7, 2, 13, 27, 55, 55, 27, 13, 1, 15, 35, 91, 105, 77, 49, 9, 2, 17, 44, 140, 182, 182, 140, 44, 17, 1, 19, 54, 204, 294, 378, 336, 156, 81, 11, 2, 21, 65, 285, 450, 714, 714, 450, 285, 65, 21, 1, 23, 77, 385, 660 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..70.

FORMULA

T(n,k)=binom(n,k)[3n-(-1)^k*(n-2*k)]/(2n) (1<=k<=n).

EXAMPLE

First 3 rows of the triangle are (1; 3,2; 5,5,1) since [1,0,0; 1,1,0; 1,2,1] * [1,0,0; 2,2,0; 0,1,1] = [1,0,0; 3,2,0; 5,5,1].

First few rows of the triangle are:

1;

3, 2;

5, 5, 1;

7, 9, 5, 2;

9, 14, 14, 9, 1;

11, 20, 30, 25, 7, 2;

13, 27, 55, 55, 27, 13, 1;

15, 35, 91, 105, 77, 49, 9, 2;

...

MAPLE

T:=(n, k)->binomial(n, k)*(3*n-(-1)^k*(n-2*k))/2/n: for n from 1 to 12 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form

CROSSREFS

Cf. A124730, A052940.

Sequence in context: A205401 A095006 A159587 * A167552 A094787 A132778

Adjacent sequences:  A124729 A124730 A124731 * A124733 A124734 A124735

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson & Roger L. Bagula, Nov 05 2006

EXTENSIONS

Edited by N. J. A. Sloane, Nov 24 2006

STATUS

approved

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Last modified September 23 17:50 EDT 2017. Contains 292363 sequences.