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Lucas multiplication table

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This article is under construction.            

Please do not rely on any information it contains.            


The entries of the th row of the Lucas multiplication table are defined as

where is the th Lucas number (A000032).

Lucas multiplication triangular table

In the table below, numbers that are 2 short of the square of a Lucas number are given a dashed black border, while those that are 2 over the square of a Lucas number are given a thick, solid border. The squares of Lucas numbers are given a thin, solid border. (The squares of the Lucas numbers are in A001254.)

A??????: Row sums
1 1
3 9 12
4 12 16 32
7 21 28 49 105
11 33 44 77 121 286
18 54 72 126 198 324 792
29 87 116 203 319 522 841 2117
47 141 188 329 517 846 1363 2209 5640
76 228 304 532 836 1368 2204 3572 5776 14896
123 369 492 861 1353 2214 3567 5781 9348 15129 39237


A180485 Lucas multiplication table as a triangle read by rows , with being a Lucas number (A000032).

{1, 3, 9, 4, 12, 16, 7, 21, 28, 49, 11, 33, 44, 77, 121, 18, 54, 72, 126, 198, 324, 29, 87, 116, 203, 319, 522, 841, 47, 141, 188, 329, 517, 846, 1363, 2209, 76, 228, 304, 532, ...}

An important difference from the Fibonacci multiplication table is that the near misses to the squares don't occur in as many columns.

Row sums of Lucas multiplication triangular table

The row sums

give the sequence (A??????)

{1, 12, 32, 105, 286, 792, 2117, 5640, 14896, 39237, ...}

See also