OFFSET
1,3
COMMENTS
T_k(0) = 1 if k == 0 mod 4, but x=0 is not counted as a solution. - Robert Israel, Apr 06 2015
LINKS
C. H. Gribble, Flattened triangle, for j = 2:100 and k = 1:j-1.
FORMULA
From Robert Israel, Apr 06 2015 (Start):
a(k,j) is multiplicative in j for each odd k.
a(k,j)+1 is multiplicative in j for k divisible by 4.
a(k,j)+[j=2] is multiplicative in j for k == 2 mod 4, where [j=2] = 1 if j=2, 0 otherwise.
a(1,j) = 1.
a(3,2^m) = 1.
a(3,p^m) = p^floor(m/2)+1 if p is a prime > 3.
a(4,p^m) = p^floor(m/2)+1 if p is a prime > 2.
a(5,p) = 3 if p is in A045468, 1 for other primes p. (End)
EXAMPLE
The triangle of numbers is:
.....k..1..2..3..4..5..6..7..8..9.10
..j..
..2.....1
..3.....1..2
..4.....1..2..1
..5.....1..2..2..2
..6.....1..4..1..5..1
..7.....1..2..2..2..1..4
..8.....1..4..1..7..1..4..1
..9.....1..2..3..4..1..6..1..4
.10.....1..4..2..5..1..8..1..5..2
.11.....1..2..2..2..3..4..1..2..2..6
MAPLE
seq(seq(nops(select(t -> orthopoly[T](k, t)-1 mod j = 0, [$1..j-1])), k=1..j-1), j=2..20); # Robert Israel, Apr 06 2015
MATHEMATICA
Table[Length[Select[Range[j-1], Mod[ChebyshevT[k, #]-1, j] == 0&]], {j, 2, 20}, {k, 1, j-1}] // Flatten (* Jean-François Alcover, Mar 27 2019, after Robert Israel *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Christopher Hunt Gribble, Aug 27 2009
EXTENSIONS
Sequence and definition corrected by Christopher Hunt Gribble, Sep 10 2009
Minor edit by N. J. A. Sloane, Sep 13 2009
STATUS
approved