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A214984
Array: T(m,n) = (F(m) + F(2*m) + ... + F(n*m))/F(m), by antidiagonals, where F = A000045 (Fibonacci numbers).
6
1, 2, 1, 4, 4, 1, 7, 12, 5, 1, 12, 33, 22, 8, 1, 20, 88, 94, 56, 12, 1, 33, 232, 399, 385, 134, 19, 1, 54, 609, 1691, 2640, 1487, 342, 30, 1, 88, 1596, 7164, 18096, 16492, 6138, 872, 48, 1, 143, 4180, 30348, 124033, 182900, 110143, 25319, 2256, 77, 1
OFFSET
1,2
COMMENTS
col 1: A001612 (except for initial term)
row 1: A000071
row 2: A027941
row 3: A049652
row 4: A092521
row 6: A049664
row 8: A156093 without minus signs
LINKS
FORMULA
For odd-numbered rows (m odd):
T(m,n) = (F(m*n+m) + F(m*n) - F(m))/(F(m)*L(m)).
For even-numbered rows (m even):
T(m,n) = (F(m*n+m) - F(m*n) - F(m))/(F(m)*(L(m)-2)).
EXAMPLE
Northwest corner:
1...2....4.....7......12......20
1...4....12....33.....88......232
1...5....22....94.....399.....1691
1...8....56....385....2640....18096
1...12...134...1487...16492...182900
MATHEMATICA
F[n_] := Fibonacci[n]; L[n_] := LucasL[n];
t[m_, n_] := (1/F[m])*Sum[F[m*k], {k, 1, n}]
TableForm[Table[t[m, n], {m, 1, 10}, {n, 1, 10}]]
Flatten[Table[t[k, n + 1 - k], {n, 1, 12}, {k, 1, n}]]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Oct 28 2012
STATUS
approved