OFFSET
0,5
COMMENTS
Main diagonal is A036765. - Paul D. Hanna, Nov 18 2016
FORMULA
a(n, k) = a(n-1, k) + a(n-1, k-1) + a(n-1, k-2) + a(n-1, k-3) with a(0, 0)=1 and a(n, k)=0 if n < k or k < 0.
EXAMPLE
Triangle begins:
1;
1, 1;
1, 2, 2;
1, 3, 5, 5;
1, 4, 9, 14, 13;
1, 5, 14, 28, 40, 36;
...
MATHEMATICA
a[n_, k_] /; 0 <= k <= n = a[n, k] = a[n - 1, k] + a[n - 1, k - 1] + a[n - 1, k - 2] + a[n - 1, k - 3]; a[0, 0] = 1; a[_, _] = 0;
Table[a[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jul 30 2018 *)
PROG
(Sage) # uses[riordan_array from A256893]
M = riordan_array(1, x/(1+x+x^2+x^3), 12).inverse()
for m in M[1:]:
print([r for r in reversed(list(m)) if r != 0]) # Peter Luschny, Aug 17 2016
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Henry Bottomley, Sep 21 2001
EXTENSIONS
Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 17 2007
STATUS
approved