login
A180485
Lucas multiplication table as a triangle read by rows T(n, k) = L(n)L(k), with L(n) being a Lucas number (A000032).
0
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, 836, 1368, 2204, 3572, 5776, 123, 369, 492, 861, 1353, 2214, 3567, 5781, 9348, 15129
OFFSET
1,2
COMMENTS
For a row indexed by a prime number p, each number in that row is congruent to L(n) mod p. This follows from Theorem 34.9 in [Koshy, 2001] (a book which contains many other interesting relations pertaining to multiples of Lucas and Fibonacci numbers).
REFERENCES
T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley & Sons, 2001, Chapter 34, "Lucas and Fibonacci Congruences" pages 402-414.
EXAMPLE
First few rows of triangle are
{{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}}
...
Example: T(8,7) = 1363 = 47 * 29
MATHEMATICA
ColumnForm[Table[LucasL[k]*LucasL[n], {k, 12}, {n, k}], Center]
CROSSREFS
Sequence in context: A011428 A070356 A143237 * A370464 A357254 A367305
KEYWORD
easy,nonn,tabl
AUTHOR
Alonso del Arte, Sep 07 2010
STATUS
approved