|
Search: id:A104583
|
|
|
| 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
|
|
| 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
(list; table; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
FORMULA
|
T(i, j)=(i-j+1)^2 if j<=i and j is odd; 2(i-j+1)^2 if j<=i and j is even; 0 if j>i. - Emeric Deutsch (deutsch(AT)duke.poly.edu), 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 (i-j+1)^2 elif j<=i and j mod 2 =0 then 2*(i-j+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 (Deutsch)
|
|
CROSSREFS
|
Cf. A002411.
Row sums yield the pentagonal pyramidal numbers (A002411).
Sequence in context: A082156 A114577 A101690 this_sequence A097664 A052915 A130273
Adjacent sequences: A104580 A104581 A104582 this_sequence A104584 A104585 A104586
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 16 2005
|
|
EXTENSIONS
|
More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 23 2005
|
|
|
Search completed in 0.002 seconds
|
