%I #6 May 03 2012 12:22:55
%S 1,2,2,3,4,2,4,6,5,2,5,8,7,5,2,6,10,10,8,5,2,7,12,12,11,8,5,2,8,14,15,
%T 13,11,8,5,2,9,16,17,17,14,11,8,5,2,10,18,20,19,18,14,11,8,5,2,11,20,
%U 22,22,20,18,14,11,8,5,2,12,22,25,25,23,20,18,14,11,8,5,2,13
%N Rectangular array: R(n,k)=[n/F(1)]+[n/F(2)]+...+[n/F(k)], where [ ]=floor and F=A000045 (Fibonacci numbers), by antidiagonals.
%C For n>=1, row n is a homogeneous linear recurrence sequence with palindromic recurrence coefficients in the sense described at A211701. The sequence approached as a limit of the rows is described in the Comments section of A175346.
%e Northwest corner:
%e 1...2...3...4....5....6....7
%e 2...4...6...8....10...12...15
%e 2...5...7...10...12...15...17
%e 2...5...8...11...13...17...19
%e 2...5...8...11...14...18...20
%e 2...5...8...11...14...18...20
%t f[n_, m_] := Sum[Floor[n/Fibonacci[k]], {k, 1, m}]
%t TableForm[Table[f[n, m], {m, 1, 20}, {n, 1, 16}]]
%t Flatten[Table[f[n + 1 - m, m], {n, 1, 14}, {m, 1, n}]]
%Y Cf. A211701.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Apr 19 2012