OFFSET
1,2
COMMENTS
LINKS
Clark Kimberling, Antidiagonals n = 1..60, flattened
FORMULA
T(n,k) = 5*T(n,k-1)-9*T(n,k-2)+7*T(n,k-3)-2*T(n,k-4).
G.f. for row n: f(x)/g(x), where f(x) = x*(-1 + 2^n + x + (-2 + 2^n)*x^2) and g(x) = (1 - 2*x)(1 - x )^3.
EXAMPLE
Northwest corner (the array is read by falling antidiagonals):
1....6.....21....58.....141
3....16....51....132....307
7....36....111...280....639
15...76....231...576....1303
31...156...471...1168...2631
MATHEMATICA
b[n_] := 2 n - 1; c[n_] := -1 + 2^n;
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}] (* A213753 *)
Table[t[n, n], {n, 1, 40}] (* A213754 *)
s[n_] := Sum[t[i, n + 1 - i], {i, 1, n}]
Table[s[n], {n, 1, 50}] (* A213755 *)
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Jun 20 2012
STATUS
approved