

A232656


The number of pairs of numbers below n that, when generating a Fibonaccilike sequence modulo n, contain zeros.


3



1, 4, 9, 16, 21, 36, 49, 40, 81, 84, 101, 96, 85, 196, 189, 136, 145, 180, 325, 336, 153, 404, 529, 216, 521, 340, 729, 496, 393, 756, 901, 520, 509, 292, 1029, 384, 685, 652, 765, 840, 801, 612, 1849, 1016, 1701, 1060, 737, 504, 2401, 2084, 1305, 1360, 1405, 1476, 521, 1096, 1629, 1572
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OFFSET

1,2


COMMENTS

a(n) = n^2 iff n is in A064414, a(n) is not equal to n^2 iff n is in A230457.


LINKS



FORMULA



EXAMPLE

The sequence 2,1,3,4,2,1 is the sequence of Lucas numbers modulo 5. Lucas numbers are never divisible by 5. The 4 pairs (2,1), (1,3), (3,4), (4,2) are the only pairs that can generate a sequence modulo 5 that doesn't contain zeros. Thus, a(5) = 21, as 21 other pairs generate sequences that do contain zeros.
Any Fibonacci like sequence contains elements divisible by 2, 3, or 4. Thus, a(2) = 4, a(3) = 9, a(4) = 16.


MATHEMATICA

fibLike[list_] := Append[list, list[[1]] + list[[2]]]; Table[k^2 Count[Flatten[Table[Count[Nest[fibLike, {n, m}, k^2]/k, _Integer], {n, k  1}, {m, k  1}]], 0], {k, 70}]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



