A054500 -id:A054500 - cp's OEIS frontend

A054501 Multiplicity sequence for classification of nonattacking queens on n X n toroidal board.

1, 10, 28, 44, 26, 52, 338, 676, 34, 68, 578, 1156, 2312, 76, 1444, 2888, 92, 2116, 4232, 50, 100, 250, 500, 1000, 1250, 2500, 5000, 58, 116, 1682, 3364, 6728

Offset: 1

Matthias Engelhardt

See comments and references for A054500.

Cf. A054500, A054502, A053994, A007705, A006841.

More terms from Matthias Engelhardt, Jan 11 2001

A054502 Counting sequence for classification of nonattacking queens on n X n toroidal board.

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 3, 5, 1, 3, 23, 30, 40, 4, 132, 218, 5, 1859, 29517, 1, 2, 9, 18, 51, 470, 7170, 387830, 1, 6, 1215, 121487, 89997968

Offset: 1

Matthias Engelhardt

See comments and references for A054500.

Cf. A054500, A054501, A053994, A007705, A006841.

More terms from Matthias Engelhardt, Jan 11 2001

A091685 Sieve out 6n+1 and 6n-1.

Original entry on oeis.org

0, 1, 0, 0, 0, 5, 0, 7, 0, 0, 0, 11, 0, 13, 0, 0, 0, 17, 0, 19, 0, 0, 0, 23, 0, 25, 0, 0, 0, 29, 0, 31, 0, 0, 0, 35, 0, 37, 0, 0, 0, 41, 0, 43, 0, 0, 0, 47, 0, 49, 0, 0, 0, 53, 0, 55, 0, 0, 0, 59, 0, 61, 0, 0, 0, 65, 0, 67, 0, 0, 0, 71, 0, 73, 0, 0, 0, 77, 0, 79, 0, 0, 0, 83, 0, 85, 0, 0, 0, 89, 0

Offset: 0

Paul Barry, Jan 28 2004

Completely multiplicative with a(2) = a(3) = 0, a(p) = p otherwise. - David W. Wilson, Jun 12 2005

Antti Karttunen, Table of n, a(n) for n = 0..10000
Index to divisibility sequences.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,2,0,0,0,0,0,-1).

Cf. A007310 (nonzero terms), A047229 (positions of zeros), A054500.

Table[n Boole[Or[# == 1, # == 5] &@ Mod[n, 6]], {n, 0, 90}] (* or *)
CoefficientList[Series[x (x^2 + 1) (x^8 - x^6 + 6 x^4 - x^2 + 1)/((x - 1)^2*(1 + x)^2*(1 + x + x^2)^2*(x^2 - x + 1)^2), {x, 0, 90}], x] (* Michael De Vlieger, Jul 24 2017 *)

a(n)=if(gcd(n,6)==1,n,0) \\ Charles R Greathouse IV, Jun 28 2015

from sympy import gcd
def a(n): return n if gcd(n, 6) == 1 else 0
print([a(n) for n in range(51)]) # Indranil Ghosh, Jul 26 2017

(define (A091685 n) (if (or (even? n) (zero? (modulo n 3))) 0 n)) ;; Antti Karttunen, Jul 24 2017

a(n) = -Product_{k=0..5} Sum_{j=1..n} w(6)^(kj), w(6) = e^(2*Pi*i/6), i = sqrt(-1).
G.f.: x*(x^2+1)*(x^8-x^6+6*x^4-x^2+1) / ( (x-1)^2 *(1+x)^2 *(1+x+x^2)^2 *(x^2-x+1)^2 ). - R. J. Mathar, Feb 14 2015
From Amiram Eldar, Dec 18 2023: (Start)
Dirichlet g.f.: zeta(s-1) * (1 - 1/2^(s-1)) * (1 - 1/3^(s-1)).
Sum_{k=1..n} a(k) ~ n^2/6. (End)

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A054501 Multiplicity sequence for classification of nonattacking queens on n X n toroidal board.

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A054502 Counting sequence for classification of nonattacking queens on n X n toroidal board.

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A091685 Sieve out 6n+1 and 6n-1.

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