OFFSET
1,2
COMMENTS
LINKS
Clark Kimberling, Antidiagonals n = 1..80, flattened
FORMULA
T(n,k) = 4*T(n,k-1)-5*T(n,k-2)+2*T(n,k-3).
G.f. for row n: f(x)/g(x), where f(x) = x*(2*n - 1 - (2*n - 3)*x) and g(x) = (1 - 2*x)(1 - x )^2.
EXAMPLE
Northwest corner (the array is read by falling antidiagonals):
1....5....15...37....83....177
3....11...29...67....145...303
5....17...43...97....207...429
7....23...57...127...269...555
9....29...71...157...331...681
11...35...85...187...393...807
MATHEMATICA
b[n_] := 2^(n - 1); c[n_] := 2 n - 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}] (* A213762 *)
Table[t[n, n], {n, 1, 40}] (* A213763 *)
s[n_] := Sum[t[i, n + 1 - i], {i, 1, n}]
Table[s[n], {n, 1, 50}] (* A213764 *)
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Jun 20 2012
STATUS
approved