OFFSET
1,4
COMMENTS
LINKS
Clark Kimberling, Antidiagonals n = 1..60, flattened
FORMULA
T[(m,n) = Fibonacci(m*n)/Fibonacci(m).
EXAMPLE
Northwest corner:
1 1 2 3 5 8
1 3 8 21 55 144
1 4 17 72 305 1292
1 7 48 329 2255 15456
1 11 122 1353 15005 166408
1 18 323 5796 104005 1866294
MATHEMATICA
F[n_] := Fibonacci[n]; t[m_, n_] := F[m*n]/F[m]
TableForm[Table[t[m, n], {m, 1, 10}, {n, 1, 10}]]
u = Table[t[k, n + 1 - k], {n, 1, 12}, {k, 1, n}];
v[n_] := Sum[F[m*(n + 1 - m)]/F[m], {m, 1, n}];
Flatten[u] (* A213978 *)
Flatten[Table[t[n, n], {n, 1, 20}]] (* A051294 *)
Table[(t[n, 5] - 5)/50, {n, 1, 20}] (* A214982 *)
Table[v[n], {n, 1, 30}] (* A214983 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Oct 27 2012
STATUS
approved