OFFSET
1,1
COMMENTS
LINKS
Clark Kimberling, Antidiagonals n=1..60, flattened
FORMULA
T(n,k) = 4*T(n,k-1)-6*T(n,k-2)+4*T(n,k-3)-T(n,k-4).
G.f. for row n: f(x)/g(x), where f(x) = x*((6*n-4) - (3*n-8)*x - (3*n-5)*x^2) and g(x) = (1-x)^4.
EXAMPLE
Northwest corner (the array is read by falling antidiagonals):
2....13...42....98....190
5....28...78....164...295
8....43...114...230...400
11...58...150...296...505
14...73...186...362...610
17...88...222...428...715
MATHEMATICA
b[n_]:=3n-2; c[n_]:=3n-1;
t[n_, k_]:=Sum[b[k-i]c[n+i], {i, 0, k-1}]
TableForm[Table[t[n, k], {n, 1, 10}, {k, 1, 10}]]
Flatten[Table[t[n-k+1, k], {n, 12}, {k, n, 1, -1}]]
r[n_]:=Table[t[n, k], {k, 1, 60}] (* A213828 *)
d=Table[t[n, n], {n, 1, 40}] (* A213829 *)
d/2 (* A005915 *)
s[n_]:=Sum[t[i, n+1-i], {i, 1, n}]
Table[s[n], {n, 1, 50}] (* A213830 *)
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Jul 04 2012
STATUS
approved