OFFSET
0,4
LINKS
Alois P. Heinz, Rows n = 0..140, flattened
J. D. H. Dickson, Discussion of two double series arising from the number of terms in determinants of certain forms, Proc. London Math. Soc., 10 (1879), 120-122.
J. D. H. Dickson, Discussion of two double series arising from the number of terms in determinants of certain forms, Proc. London Math. Soc., 10 (1879), 120-122. [Annotated scanned copy]
FORMULA
EXAMPLE
Triangle starts:
1;
1, 0;
2, 1, 0;
6, 4, 1, 1;
...
MAPLE
a:= proc(n, k) option remember; `if`(k=0, n!, `if`(n=k,
`if`(n<3, (n-1)*(n-2)/2, (n-1)*(a(n-1$2)+a(n-2$2))
+a(n-3$2)), a(n, k+1) +2*a(n-1, k) +a(n-2, k-1)))
end:
seq(seq(a(n, k), k=0..n), n=0..10); # Alois P. Heinz, Jun 24 2017
MATHEMATICA
a[n_, n_] := (-1)^n*HypergeometricPFQ[{1, -n, n+1}, {1/2}, 1/4]; a[n_, k_] := a[n, k] = a[n, k+1] + 2*a[n-1, k] + a[n-2, k-1]; Table[a[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jun 24 2015 *)
CROSSREFS
KEYWORD
AUTHOR
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Sep 29 2000
STATUS
approved