A275510 Triangle read by rows, T(n,k) = floor(n/k) - 2*floor(n/(2*k)), for n>=2 and 2<=k<=n; additionally T(1,2) = 0.

0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1

Offset

1

Links

Table of n, a(n) for n=1..79.

Formula

Let cp(n) denote the cyclotomic polynomials then Product_{k=2..n} cp(k)^T(n, k) = q-factorial(n) / q-factorial(floor(n/2))^2 (cf. A274888).

Example

The triangle starts:
[ n] [T(n,k),k=2,3,4,...] [row sum]
[ 1] [0] 0
[ 2] [1] 1
[ 3] [1, 1] 2
[ 4] [0, 1, 1] 2
[ 5] [0, 1, 1, 1] 3
[ 6] [1, 0, 1, 1, 1] 4
[ 7] [1, 0, 1, 1, 1, 1] 5
[ 8] [0, 0, 0, 1, 1, 1, 1] 4
[ 9] [0, 1, 0, 1, 1, 1, 1, 1] 6
[10] [1, 1, 0, 0, 1, 1, 1, 1, 1] 7
[11] [1, 1, 0, 0, 1, 1, 1, 1, 1, 1] 8
[12] [0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1] 7
[13] [0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1] 8
[14] [1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1] 9

Crossrefs

Cf. A274888, A275495 (row sums).

Sequence in context: A189723 A095770 A285972 * A286055 A140318 A060584

Adjacent sequences: A275507 A275508 A275509 * A275511 A275512 A275513

Keyword

nonn,tabf

Author

Peter Luschny, Jul 31 2016

Status

approved