OFFSET
1,2
COMMENTS
LINKS
Clark Kimberling, Antidiagonals n = 1..60, flattened
FORMULA
T(n,k) = 6*T(n,k-1)-13*T(n,k-2)+12*T(n,k-3)-4*T(n,k-4).
G.f. for row n: f(x)/g(x), where f(x) = -1 + 2^n - (-2 - 2^n)*x and g(x) = (1 - 3*x + 2*x^2 )^2.
EXAMPLE
Northwest corner (the array is read by falling antidiagonals):
1....6.....23....72.....201
3....16....57....170....459
7....36....125...366....975
15...76....261...758....1007
31...156...533...1542...4071
MATHEMATICA
b[n_] := -1 + 2^n; 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}] (* A213747 *)
Table[t[n, n], {n, 1, 40}] (* A213748 *)
s[n_] := Sum[t[i, n + 1 - i], {i, 1, n}]
Table[s[n], {n, 1, 50}] (* A213749 *)
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Jun 19 2012
STATUS
approved