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A281098 a(n) is the GCD of the sequence d(n) = A261327(k+n) - A261327(k) for all k. 0
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..79.

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).

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

CROSSREFS

Cf. A064680, A144433 or A195161.

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

Sequence in context: A171073 A021297 A124909 * 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

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Last modified September 22 20:30 EDT 2018. Contains 315270 sequences. (Running on oeis4.)