OFFSET
1,2
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*(2*n-1 + 4*n*x - (6*n-9)*x^2) and g(x) = (1-x)^4.
EXAMPLE
Northwest corner (the array is read by falling antidiagonals):
1....8....29....72....145
3....20...59....128...235
5....32...89....184...325
7....44...119...240...415
9....56...149...296...505
11...68...179...352...595
MATHEMATICA
b[n_]:=4n-3; c[n_]:=2n-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}] (* A213838 *)
Table[t[n, n], {n, 1, 40}] (* A213839 *)
s[n_]:=Sum[t[i, n+1-i], {i, 1, n}]
Table[s[n], {n, 1, 50}] (* A213840 *)
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Jul 05 2012
STATUS
approved