

A104569


Triangle read by rows: T(i,j) is the (i,j)entry (1 <= j <= i) of the product Q*R of the infinite lower triangular matrices Q = [1; 1,3; 1,3,1; 1 3,1,3; ...] and R = [1; 1,1; 1,1,1; 1,1,1,1; ...].


2



1, 4, 3, 5, 4, 1, 8, 7, 4, 3, 9, 8, 5, 4, 1, 12, 11, 8, 7, 4, 3, 13, 12, 9, 8, 5, 4, 1, 16, 15, 12, 11, 8, 7, 4, 3, 17, 16, 13, 12, 9, 8, 5, 4, 1, 20, 19, 16, 15, 12, 11, 8, 7, 4, 3, 21, 20, 17, 16, 13, 12, 9, 8, 5, 4, 1, 24, 23, 20, 19, 16, 15, 12, 11, 8, 7, 4, 3, 25, 24, 21, 20, 17, 16, 13
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..85.


FORMULA

For 1<=j<=i: T(i, j)=2(ij+1) if i and j are of opposite parity; T(i, j)=2(ij)+1 if both i and j are odd; T(i, j)=2(ij)+3 if both i and j are even.  Emeric Deutsch, Mar 23 2005


EXAMPLE

The first few rows of the triangle are:
1;
4, 3;
5, 4, 1;
8, 7, 4, 3;
9, 8, 5, 4, 1;
...


MAPLE

T:=proc(i, j) if j>i then 0 elif i+j mod 2 = 1 then 2*(ij)+2 elif i mod 2 = 1 and j mod 2 = 1 then 2*(ij)+1 elif i mod 2 = 0 and j mod 2 = 0 then 2*(ij)+3 else fi end: for i from 1 to 13 do seq(T(i, j), j=1..i) od; # yields sequence in triangular form # Emeric Deutsch, Mar 23 2005


CROSSREFS

Cf. A035608, A074377, A104570.
Row sums yield A074377. Columns 1, 3, 5, ... (starting at the diagonal entry) yield A042948. Columns 2, 4, 6, ... (starting at the diagonal entry) yield A014601. The product R*Q yields A104570.
Sequence in context: A075128 A074091 A177033 * A093619 A134186 A024688
Adjacent sequences: A104566 A104567 A104568 * A104570 A104571 A104572


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, Mar 16 2005


EXTENSIONS

More terms from Emeric Deutsch, Mar 23 2005


STATUS

approved



