|
Search: id:A083877
|
|
|
| A083877 |
|
Determinant of n X n matrix where the element a(i,j) = if i + j > n then 2*(i + j -n) - 1, else 2*(n + 1 - i - j). |
|
+0
1
|
|
| 1, 5, 25, 101, 385, 1397, 4921, 16949, 57409, 191909, 634777, 2081477, 6775873, 21921941, 70548793, 225995285, 721032577, 2292237893, 7264134169, 22954663973, 72350776321, 227512682165, 713919106105, 2235900497141
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
The main antidiagonal is 1, the upper left elements are increasing larger even numbers and the lower right elements are increasing larger odd numbers.
|
|
FORMULA
|
1/12 * [(4n-1)3^n - 3(-1)^n].
|
|
EXAMPLE
|
a(5) = det{ 8 6 4 2 1 / 6 4 2 1 3 / 4 2 1 3 5 / 2 1 3 5 7 / 1 3 5 7 9 } = 285.
|
|
MATHEMATICA
|
f[i_, j_, n_] := Block[{a = 2*(i + j) - 2*n - 1}, If[i + j <= n, a = Abs[a - 1]]; a]; Table[ Abs[ Det[ Table[ f[i, j, n], {i, 1, n}, {j, 1, n}]]], {n, 1, 24}]
|
|
CROSSREFS
|
Adjacent sequences: A083874 A083875 A083876 this_sequence A083878 A083879 A083880
Sequence in context: A055343 A022729 A098111 this_sequence A067971 A111641 A074419
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Robert G. Wilson v (rgwv(AT)rgwv.com), May 07 2003
|
|
|
Search completed in 0.002 seconds
|
