A281098 a(n) is the GCD of the sequence d(n) = A261327(k+n) - A261327(k) for all k.

0, 1, 1, 3, 4, 1, 3, 1, 8, 3, 5, 1, 12, 1, 7, 3, 16, 1, 9, 1, 20, 3, 11, 1, 24, 1, 13, 3, 28, 1, 15, 1, 32, 3, 17, 1, 36, 1, 19, 3, 40, 1, 21, 1, 44, 3, 23, 1, 48, 1, 25, 3, 52, 1, 27, 1, 56, 3, 29, 1, 60, 1, 31, 3, 64, 1, 33, 1, 68, 3, 35, 1, 72, 1, 37, 3, 76, 1, 39, 1

Offset

0,4

Comments

Successive sequences:

0: 0, 0, 0, 0, ... = 0 * ( )

1: 4, -3, 11, -8, ... = 1 * ( )

2: 1, 8, 3, 16, ... = 1 * ( ) A195161

3: 12, 0, 27, -3, ... = 3 * (4, 0, 9, -1, ...)

4: 4, 24, 8, 40, ... = 4 * (1, 6, 2, 10, ...) A064680

5; 28, 5, 51, 4, ... = 1 * ( )

6: 9, 48, 15, 72, ... = 3 * (3, 16, 5, 24, ...) A195161

7: 52, 12, 83, 13, ... = 1 * ( )

8: 16, 80, 24, 112, ... = 8 * (2, 10, 3, 14, ...) A064080

9: 84 21, 123, 24, ... = 3 * (28, 7, 41, 8, ...)

10: 25, 120, 35, 160, ... = 5 * (5, 24, 7, 32, ...) A195161

Links

Antti Karttunen, Table of n, a(n) for n = 0..16384

Index entries for linear recurrences with constant coefficients, signature (0,-1,0,1,0,2,0,1,0,-1,0,-1).

Formula

G.f.: -x*( -1 - x - 4*x^2 - 5*x^3 - 3*x^4 - 6*x^5 + 3*x^6 - 5*x^7 + 4*x^8 - x^9 + x^10 )/( (x^2 - x + 1)*(1 + x + x^2)*(x - 1)^2*(1 + x)^2*(1 + x^2)^2 ). - R. J. Mathar, Jan 31 2017

a(2*k) = A022998(k).

a(2*k+1) = A109007(k-1).

a(3*k) = interleave 3*k*(3 +(-1)^k)/2, 3.

a(3*k+1) = interleave 1, A166304(k).

a(3*k+2) = interleave A166138(k), 1.

a(4*k) = 4*k.

a(4*k+1) = period 3: repeat [1, 1, 3].

a(4*k+2) = 1 + 2*k.

a(4*k+3) = period 3: repeat [3, 1, 1].

a(n+12) - a(n) = 6*A131743(n+3).

a(n) = (18*n + 40 - 16*cos(n*Pi/3) + 9*n*cos(n*Pi/2) + 32*cos(2*n*Pi/3) + (18*n - 40)*cos(n*Pi) + 3*n*cos(3*n*Pi/2) - 16*cos(5*n*Pi/3))/48. - Wesley Ivan Hurt, Oct 04 2018

Mathematica

CoefficientList[Series[(-x (-1 - x - 4 x^2 - 5 x^3 - 3 x^4 - 6 x^5 + 3 x^6 - 5 x^7 + 4 x^8 - x^9 + x^10))/((x^2 - x + 1) (1 + x + x^2) (x - 1)^2*(1 + x)^2*(1 + x^2)^2), {x, 0, 79}], x] (* Michael De Vlieger, Feb 02 2017 *)

Prog

(PARI) f(n) = numerator((4 + n^2)/4);
a(n) = gcd(vector(1000, k, f(k+n) - f(k))); \\ Michel Marcus, Jan 15 2017
(PARI) A281098(n) = if(n%2, gcd((n\2)-1, 3), n>>(bitand(n, 2)/2)); \\ Antti Karttunen, Feb 15 2023

Crossrefs

Cf. A064680, A144433 or A195161.

Cf. A000012, A005408, A008586, A010701, A109007 (bisection), A016825, A165988 (via A022998), A166138, A166304, A280579.

Sequence in context: A124909 A348354 A356708 * A090279 A101667 A117378

Adjacent sequences: A281095 A281096 A281097 * A281099 A281100 A281101

Keyword

nonn,easy

Author

Paul Curtz, Jan 14 2017

Extensions

Corrected and extended by Michel Marcus, Jan 15 2017

Status

approved