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A219875
Multiplication table of the operation "n o m" = n*m + ceiling(n/phi)* ceiling(m/phi), with phi = (1+sqrt(5))/2, read by antidiagonals.
2
2, 4, 4, 5, 8, 5, 7, 10, 10, 7, 9, 14, 13, 14, 9, 10, 18, 18, 18, 18, 10, 12, 20, 23, 25, 23, 20, 12, 13, 24, 26, 32, 32, 26, 24, 13, 15, 26, 31, 36, 41, 36, 31, 26, 15, 17, 30, 34, 43, 46, 46, 43, 34, 30, 17, 18, 34, 39, 47, 55, 52, 55, 47, 39, 34, 18
OFFSET
1,1
COMMENTS
Like A101866, this operation is associative.
First rows of the table are:
1: 2, 4, 5, 7, 9, 10, 12, 13, 15, 17, ...
2: 4, 8, 10, 14, 18, 20, 24, 26, 30, 34, ...
3: 5, 10, 13, 18, 23, 26, 31, 34, 39, 44, ...
4: 7, 14, 18, 25, 32, 36, 43, 47, 54, 61, ...
5: 9, 18, 23, 32, 41, 46, 55, 60, 69, 78, ...
6:10, 20, 26, 36, 46, 52, 62, 68, 78, 88, ...
7:12, 24, 31, 43, 55, 62, 74, 81, 93, 105, ...
8:13, 26, 34, 47, 60, 68, 81, 89, 102, 115, ...
9:15, 30, 39, 54, 69, 78, 93, 102, 117, 132, ...
Row 1 is A004956.
Row 3 is A101868.
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..11325 (first 150 antidiagonals, flattened).
P. Arnoux, Some remarks about Fibonacci multiplication, Applied Mathematics Letters, Volume 2, Issue 4, 1989, Pages 319-320.
MATHEMATICA
A219875[n_, m_] := n*m + Ceiling[n / GoldenRatio] * Ceiling[m / GoldenRatio];
Table[A219875[n-m+1, m], {n, 15}, {m, n}] (* Paolo Xausa, Mar 20 2024 *)
PROG
(PARI) prod(m, n) = {phi = (1+sqrt(5))/2; return (m*n + ceil(m/phi)*ceil(n/phi)); }
CROSSREFS
Cf. A001622, A004956, A101385, A101858, A101866, A101868, A371381 (main diagonal).
Sequence in context: A349462 A340761 A035625 * A132128 A280057 A257174
KEYWORD
nonn,tabl
AUTHOR
Michel Marcus, Dec 01 2012
STATUS
approved