A256658 - OEIS

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A256658

Rectangular array by antidiagonals: row n consists of numbers k such that F(n+1) is the trace of the minimal alternating Fibonacci representation of k, where F = A000045 (Fibonacci numbers).

1, 9, 2, 14, 15, 3, 17, 23, 24, 5, 22, 28, 37, 39, 8, 27, 36, 45, 60, 63, 13, 30, 44, 58, 73, 97, 102, 21, 35, 49, 71, 94, 118, 157, 165, 34, 43, 57, 79, 115, 152, 191, 254, 267, 55, 48, 70, 92, 128, 186, 246, 309, 411, 432, 89, 51, 78, 113, 149, 207, 301

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OFFSET

1,2

COMMENTS

See A256655 for definitions. This array and the array at A256659 partition the positive integers. The row differences are Fibonacci numbers. The columns satisfy the Fibonacci recurrence x(n) = x(n-1) + x(n-2).

LINKS

Table of n, a(n) for n=1..61.

EXAMPLE

Northwest corner:

1 9 14 17 22 27 30 35 43

2 15 23 28 36 44 49 57 70

3 24 37 45 58 71 79 92 113

5 39 69 73 94 115 128 149 183

8 63 97 118 152 186 207 241 296

13 102 157 191 246 301 335 390 479

MATHEMATICA

b[n_] = Fibonacci[n]; bb = Table[b[n], {n, 1, 70}];