A089145 -id:A089145 - cp's OEIS frontend

A168061 Denominator of (n+3) / ((n+2) * (n+1) * n).

3, 24, 10, 120, 105, 112, 252, 720, 165, 1320, 858, 728, 1365, 3360, 680, 4896, 2907, 2280, 3990, 9240, 1771, 12144, 6900, 5200, 8775, 19656, 3654, 24360, 13485, 9920, 16368, 35904, 6545, 42840, 23310, 16872, 27417, 59280, 10660, 68880, 37023, 26488, 42570

Offset: 1

Vladimir Joseph Stephan Orlovsky, Nov 17 2009

Numerator of ((n+3)/(n+2)/(n+1)/n) = A060789(n).

G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,4,0,0,0,0,0,-6,0,0,0,0,0,4,0,0,0,0,0,-1).

Cf. A060789.

List([1..10^3],n->DenominatorRat((n+3)/(n+2)/(n+1)/n)); # Muniru A Asiru, Feb 04 2018

seq(denom((n+3)/(n+2)/(n+1)/n), n=1..10^3); # Muniru A Asiru, Feb 04 2018

Table[Denominator[(n+3)/(n+2)/(n+1)/n],{n,60}]
LinearRecurrence[{0,0,0,0,0,4,0,0,0,0,0,-6,0,0,0,0,0,4,0,0,0,0,0,-1},{3,24,10,120,105,112,252,720,165,1320,858,728,1365,3360,680,4896,2907,2280,3990,9240,1771,12144,6900,5200},50] (* Harvey P. Dale, Apr 06 2017 *)

vector(50, n, denominator(((n+3)/(n+2)/(n+1)/n))) \\ Colin Barker, Feb 04 2018

Vec(x*(3 + 24*x + 10*x^2 + 120*x^3 + 105*x^4 + 112*x^5 + 240*x^6 + 624*x^7 + 125*x^8 + 840*x^9 + 438*x^10 + 280*x^11 + 375*x^12 + 624*x^13 + 80*x^14 + 336*x^15 + 105*x^16 + 40*x^17 + 30*x^18 + 24*x^19 + x^20) / ((1 - x)^4*(1 + x)^4*(1 - x + x^2)^4*(1 + x + x^2)^4) + O(x^60)) \\ Colin Barker, Feb 04 2018

a(n) = 4*a(n-6) -6*a(n-12) +4*a(n-18) -a(n-24) = A007531(n+2)/A089145(n). - R. J. Mathar, Nov 18 2009

G.f.: x*(3 + 24*x + 10*x^2 + 120*x^3 + 105*x^4 + 112*x^5 + 240*x^6 + 624*x^7 + 125*x^8 + 840*x^9 + 438*x^10 + 280*x^11 + 375*x^12 + 624*x^13 + 80*x^14 + 336*x^15 + 105*x^16 + 40*x^17 + 30*x^18 + 24*x^19 + x^20) / ((1 - x)^4*(1 + x)^4*(1 - x + x^2)^4*(1 + x + x^2)^4). - Colin Barker, Feb 04 2018

A306764 a(n) is a sequence of period 12: repeat [1, 1, 6, 2, 1, 3, 2, 2, 3, 1, 2, 6].

Original entry on oeis.org

1, 1, 6, 2, 1, 3, 2, 2, 3, 1, 2, 6, 1, 1, 6, 2, 1, 3, 2, 2, 3, 1, 2, 6, 1, 1, 6, 2, 1, 3, 2, 2, 3, 1, 2, 6, 1, 1, 6, 2, 1, 3, 2, 2, 3, 1, 2, 6, 1, 1, 6, 2, 1, 3, 2, 2, 3, 1, 2, 6, 1, 1, 6, 2, 1, 3, 2, 2, 3, 1, 2, 6

Offset: 0

Paul Curtz, Mar 08 2019

a(1) to a(12) is a palindrome.
A089145(n) = A089128(n+3).
A089128(n) = A089145(n+3).
a(1) + a(2) + a(3) + a(4) = a(5) + a(6) + a(7) + a(8) = a(9) + a(10) + a(11) + a(12) = 10.

			a(0) =  6/6  = 1;
a(1) = 10/10 = 1;
a(2) = 30/5  = 6;
a(3) = 42/21 = 2.

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

Cf. A064038, A089128 and A089145 (shifted bisections), A306368, A010692.

PadRight[{},120,{1,1,6,2,1,3,2,2,3,1,2,6}] (* or *) LinearRecurrence[ {0,0,1,0,0,-1,0,0,1},{1,1,6,2,1,3,2,2,3},120] (* Harvey P. Dale, Dec 16 2021 *)

Vec((1 + x + 6*x^2 + x^3 - 3*x^5 + x^6 + 2*x^7 + 6*x^8) / ((1 - x)*(1 + x^2)*(1 + x + x^2)*(1 - x^2 + x^4)) + O(x^80)) \\ Colin Barker, Dec 11 2019

a(n) = 2*A064038(n+3)/A306368(n).
a(n) = interleave A089128(n-1), A089128(n+1).
a(n) = interleave A089145(n+2), A089145(n-2).
From Colin Barker, Dec 09 2019: (Start)
G.f.: (1 + x + 6*x^2 + x^3 - 3*x^5 + x^6 + 2*x^7 + 6*x^8) / ((1 - x)*(1 + x^2)*(1 + x + x^2)*(1 - x^2 + x^4)).
a(n) = a(n-3) - a(n-6) + a(n-9) for n>8.
(End)

cp's OEIS Frontend

A168061 Denominator of (n+3) / ((n+2) * (n+1) * n).

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A306764 a(n) is a sequence of period 12: repeat [1, 1, 6, 2, 1, 3, 2, 2, 3, 1, 2, 6].

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