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%I #8 Jun 09 2023 08:05:40
%S 1,2,1,3,3,1,4,4,3,1,5,6,5,3,1,6,7,7,5,3,1,7,9,8,7,5,3,1,8,10,11,9,7,
%T 5,3,1,9,12,12,12,9,7,5,3,1,10,13,14,13,12,9,7,5,3,1,11,15,16,15,13,
%U 12,9,7,5,3,1,12,16,18,17,16,13,12,9,7,5,3,1,13,18,19,20,18,16
%N Rectangular array: R(n,k)=[n/F(2)]+[n/F(3)]+...+[n/F(k+1)], 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 begins with 1,3,5,7,9,12,13,16,18,21,22,25.
%e Northwest corner:
%e 1...2...3...4...5...6....7....8
%e 1...3...4...6...7...9....10...12
%e 1...3...5...7...8...11...12...14
%e 1...3...5...7...9...12...13...15
%e 1...3...5...7...9...12...13...16
%t f[n_, m_] := Sum[Floor[n/Fibonacci[k + 1]], {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. A000045, A211701.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Apr 20 2012
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