

A104583


Triangle read by rows: T(i,j) is the (i,j)entry (1 <= j <= i) of the product A*B of the matrices A = [1; 3,1; 5,3,1; 7,5,3,1; ...]; B = [1; 1,2; 1,2,1; 1,2,1,2; ...] (both infinite lower triangular matrices).


0



1, 4, 2, 9, 8, 1, 16, 18, 4, 2, 25, 32, 9, 8, 1, 36, 50, 16, 18, 4, 2, 49, 72, 25, 32, 9, 8, 1, 64, 98, 36, 50, 16, 18, 4, 2, 81, 128, 49, 72, 25, 32, 9, 8, 1, 100, 162, 64, 98, 36, 50, 16, 18, 4, 2, 121, 200, 81, 128, 49, 72, 25, 32, 9, 8, 1, 144, 242, 100, 162, 64, 98, 36, 50, 16, 18
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OFFSET

0,2


LINKS



FORMULA

T(i, j) = (ij+1)^2 if j <= i and j is odd; 2(ij+1)^2 if j <= i and j is even; 0 if j > i.  Emeric Deutsch, Mar 23 2005


EXAMPLE

The first few rows are:
1;
4, 2;
9, 8, 1;
16, 18, 4, 2;
25, 32, 9, 8, 1;
36, 50, 16, 18, 4, 2;
49, 72, 25, 32, 9, 8, 1;
...


MAPLE

T:=proc(i, j) if j<=i and j mod 2=1 then (ij+1)^2 elif j<=i and j mod 2 =0 then 2*(ij+1)^2 else 0 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

Row sums yield the pentagonal pyramidal numbers (A002411).


KEYWORD



AUTHOR



EXTENSIONS



STATUS

approved



