|
| |
|
|
A279010
|
|
Alternating Jacobsthal triangle A_3(n,k) read by rows.
|
|
2
|
|
|
|
1, 1, 1, 3, 0, 1, 3, 3, -1, 1, 9, 0, 4, -2, 1, 9, 9, -4, 6, -3, 1, 27, 0, 13, -10, 9, -4, 1, 27, 27, -13, 23, -19, 13, -5, 1, 81, 0, 40, -36, 42, -32, 18, -6, 1, 81, 81, -40, 76, -78, 74, -50, 24, -7, 1, 243, 0, 121, -116, 154, -152, 124, -74, 31, -8, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,4
|
|
|
LINKS
|
Table of n, a(n) for n=0..65.
Kyu-Hwan Lee, Se-jin Oh, Catalan triangle numbers and binomial coefficients, arXiv:1601.06685 [math.CO], 2016.
|
|
|
EXAMPLE
|
Triangle begins:
1;
1, 1;
3, 0, 1;
3, 3, -1, 1;
9, 0, 4, -2, 1;
9, 9, -4, 6, -3, 1;
27, 0, 13, -10, 9, -4, 1;
27, 27, -13, 23, -19, 13, -5, 1;
81, 0, 40, -36, 42, -32, 18, -6, 1;
81, 81, -40, 76, -78, 74, -50, 24, -7, 1;
243, 0, 121, -116, 154, -152, 124, -74, 31, -8, 1;
...
|
|
|
MATHEMATICA
|
A[n_, 0] := 3^Floor[n/2];
A[n_, k_] /; (k<0 || t>n) = 0;
A[n_, n_] = 1;
A[n_, k_] := A[n, k] = A[n-1, k-1] - A[n-1, k];
Table[A[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Aug 12 2018 *)
|
|
|
CROSSREFS
|
If initial column is omitted, this is very like the Riordan matrix A191582.
Cf. A112468, A279006, A279009.
Sequence in context: A218603 A207032 A169940 * A121481 A121469 A091867
Adjacent sequences: A279007 A279008 A279009 * A279011 A279012 A279013
|
|
|
KEYWORD
|
sign,tabl
|
|
|
AUTHOR
|
N. J. A. Sloane, Dec 07 2016
|
|
|
STATUS
|
approved
|
| |
|
|
