A131800 -id:A131800 - cp's OEIS frontend

A138279 Last digit of A136324. After 0, 1, period 4: repeat [1, 2, 5, 6] = A131800.

0, 1, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6

Offset: 0

Paul Curtz, May 06 2008

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

Cf. A131800, A136324.

[0,1] cat &cat [[1, 2, 5, 6]^^30]; // Wesley Ivan Hurt, Jul 08 2016

0,1,seq(op([1, 2, 5, 6]), n=0..50); # Wesley Ivan Hurt, Jul 08 2016

PadRight[{0,1}, 120, {5,6,1,2}] (* Harvey P. Dale, Jul 14 2014 *)

PARI
```
a(n)=if(n>1,[6,1,2,5][n%4+1],n)
```

concat(0, Vec((x+x^2+2*x^3+5*x^4+5*x^5)/(1-x^4) + O(x^99))) \\ Altug Alkan, Jul 08 2016

From Wesley Ivan Hurt, Jul 08 2016: (Start)
G.f.: (x+x^2+2*x^3+5*x^4+5*x^5)/(1-x^4).
a(n) = a(n-4) for n>5.
a(n) = (7 - I^(2*n) + (2 + 2*I)*I^(-n) + (2 - 2*I)*I^n)/2 for n>1. (End)

A173315 Inverse binomial transform of A131800.

Original entry on oeis.org

1, 1, 2, -4, 0, 16, -48, 96, -160, 256, -448, 896, -1920, 4096, -8448, 16896, -33280, 65536, -130048, 260096, -522240, 1048576, -2101248, 4202496, -8396800, 16777216, -33538048, 67076096, -134184960, 268435456, -536936448, 1073872896, -2147614720, 4294967296

Offset: 0

Paul Curtz, Feb 16 2010

Index entries for linear recurrences with constant coefficients, signature (-4, -6, -4).

Cf. A106603.

A131800(n) = A000111(n+2) mod 10.

a(n)= -4*a(n-1) -6*a(n-2) -4*a(n-3), n>3. G.f.: (5*x+12*x^2+14*x^3+1)/((2*x+1)*(2*x^2+2*x+1)).

Extended, keyword:sign added by R. J. Mathar, Feb 24 2010

A010696 Periodic sequence: Repeat 2,6.

Original entry on oeis.org

2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2

Offset: 0

N. J. A. Sloane

Original name: Period 2.

Also continued fraction expansion of 1+(2/3)*sqrt(3). - Bruno Berselli, Sep 22 2011

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

Cf. A174114. [From Reinhard Zumkeller, Mar 08 2010]

PadRight[{}, 100, {2, 6}] (* Paolo Xausa, Feb 22 2024 *)

G.f.: ( -2-6*x ) / ( (x-1)*(1+x) ). - R. J. Mathar, Jul 07 2011

a(n) = a(-n) = 2*A010684(n) = A131800(2n+1) = A010123(2n+2). - Bruno Berselli, Sep 22 2011

Definition rewritten by Bruno Berselli, Sep 22 2011

A180343 a(0)=-4; a(n+1) = 2*a(n) + period 4: repeat 6,1,2,5.

Original entry on oeis.org

-4, -2, -3, -4, -3, 0, 1, 4, 13, 32, 65, 132, 269, 544, 1089, 2180, 4365, 8736, 17473, 34948, 69901, 139808, 279617, 559236, 1118477, 2236960, 4473921, 8947844, 17895693, 35791392, 71582785, 143165572, 286331149, 572662304, 1145324609, 2290649220, 4581298445

Offset: 0

Paul Curtz, Jan 18 2011

Period 4:repeat 6,1,2,5 = A131800(n-1).

			a(1) = 2*(-4) + 6 = -2;
a(2) = 2*(-2) + 1 = -3;
a(3) = 2*(-3) + 2 = -4;
a(4) = 2*(-4) + 5 = -3;
a(5) = 2*(-3) + 6 =  0.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,0,0,1,-2).

I:=[-4, -2, -3, -4, -3]; [n le 5 select I[n] else 2*Self(n-1)+Self(n-4)-2*Self(n-5): n in [1..40]]; // Vincenzo Librandi, Jun 17 2012

A112030 := proc(n) (2+(-1)^n)*(-1)^floor(n/2) ; end proc:
A180343 := proc(n) -2/5*A112030(n+1)-(-1)^n/6-7/2+2^n/15 ; end proc: # R. J. Mathar, Jan 18 2011

CoefficientList[Series[(-4+6*x+x^2+2*x^3+9*x^4)/((x-1)*(2*x-1)*(1+x)*(x^2+1)),{x,0,40}],x] (* Vincenzo Librandi, Jun 17 2012 *)
LinearRecurrence[{2,0,0,1,-2},{-4,-2,-3,-4,-3},40] (* Harvey P. Dale, Sep 06 2020 *)

G.f.: ( -4 + 6*x + x^2 + 2*x^3 + 9*x^4 ) / ( (x-1)*(2*x-1)*(1+x)*(x^2+1) ). - R. J. Mathar, Jan 18 2011
a(n) = 2*a(n-1) + A131800(n+2).
a(n) = a(n-4) + 2^n.
a(n) = a(n-2) + 4*A007909(n) (A007909(0)=0). From second -3.
a(n) = -2*A112030(n+1)/5 - (-1)^n/6 - 7/2 + 2^n/15. - R. J. Mathar, Jan 18 2011
a(n) = 2*a(n-1) + a(n-4) - 2*a(n-5). - Vincenzo Librandi, Jun 17 2012

A178131 Decimal expansion of (11+3*sqrt(21))/17.

Original entry on oeis.org

1, 4, 5, 5, 7, 4, 8, 6, 5, 2, 0, 5, 1, 0, 3, 0, 5, 8, 9, 3, 9, 7, 8, 9, 0, 6, 8, 1, 2, 4, 6, 1, 1, 9, 1, 4, 5, 1, 1, 4, 9, 0, 4, 1, 0, 1, 7, 8, 2, 5, 8, 3, 2, 7, 6, 9, 3, 0, 6, 8, 9, 7, 8, 6, 5, 7, 1, 8, 0, 0, 3, 1, 0, 3, 9, 0, 7, 8, 3, 0, 9, 7, 6, 3, 6, 0, 6, 3, 8, 0, 4, 6, 1, 6, 4, 9, 0, 2, 9, 9, 8, 8, 4, 2, 8

Offset: 1

Klaus Brockhaus, May 20 2010

Continued fraction expansion of (11+3*sqrt(21))/17 is A131800.

			(11+3*sqrt(21))/17 = 1.45574865205103058939...

Cf. A010477 (decimal expansion of sqrt(21)), A131800 (repeat 1, 2, 5, 6).

cp's OEIS Frontend

A138279 Last digit of A136324. After 0, 1, period 4: repeat [1, 2, 5, 6] = A131800.

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A173315 Inverse binomial transform of A131800.

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A010696 Periodic sequence: Repeat 2,6.

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A180343 a(0)=-4; a(n+1) = 2*a(n) + period 4: repeat 6,1,2,5.

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A178131 Decimal expansion of (11+3*sqrt(21))/17.

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