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Rectangular array: R(n,k)=[n/F(1)]+[n/F(2)]+...+[n/F(k)], where [ ]=floor and F=A000045 (Fibonacci numbers), by antidiagonals.
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%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