A214978 Array T(m,n) = Fibonacci(m*n)/Fibonacci(m), by antidiagonals; transpose of A028412.
1, 1, 1, 2, 3, 1, 3, 8, 4, 1, 5, 21, 17, 7, 1, 8, 55, 72, 48, 11, 1, 13, 144, 305, 329, 122, 18, 1, 21, 377, 1292, 2255, 1353, 323, 29, 1, 34, 987, 5473, 15456, 15005, 5796, 842, 47, 1, 55, 2584, 23184, 105937, 166408, 104005, 24447, 2208, 76, 1, 89
Offset: 1
Examples
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
Links
- Clark Kimberling, Antidiagonals n = 1..60, flattened
Programs
-
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 *)
Formula
T(m,n) = Fibonacci(m*n)/Fibonacci(m).
Comments