A084338 -id:A084338 - cp's OEIS frontend

A007829 From random walks on complete directed triangle.

0, 0, 0, 0, 0, 6, 8, 28, 44, 100, 162, 318, 514, 942, 1518, 2672, 4302, 7380, 11882, 20040, 32276, 53810, 86710, 143396, 231204, 380152, 613286, 1004188, 1620864, 2645928, 4272744, 6959326, 11242518, 18281222, 29542078, 47978666, 77552928, 125836374, 203445784

Offset: 0

Eric Bussian [ ebussian(AT)math.gatech.edu ]

Sean A. Irvine, Table of n, a(n) for n = 0..500
E. Bussian, Email to N. J. A. Sloane, Oct. 1994
Index entries for linear recurrences with constant coefficients, signature (2,3,-6,-4,5,5,-2,-2).

Cf. A000931, A084338.

m:=35; S:=series(2*x^5*(3-2*x-3*x^2)/((1-x)*(1-x-x^2)*(1-2*x^2)*(1-x^2-x^3)), x, m+1): seq(coeff(S, x, j), j=0..m); # G. C. Greubel, Mar 11 2020

b[n_]:= b[n]= If[n==0, 1, If[n<3, 0, b[n-2] +b[n-3]]]; Table[2*(2 +Fibonacci[n+2] -2^Floor[n/2] -p[n+7] -p[n+5]), {n,0,35}] (* G. C. Greubel, Mar 11 2020 *)

def A007829_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 2*x^5*(3-2*x-3*x^2)/((1-x)*(1-x-x^2)*(1-2*x^2)*(1-x^2-x^3)) ).list()
A007829_list(35) # G. C. Greubel, Mar 11 2020

From Colin Barker, Feb 03 2018: (Start)
G.f.: 2*x^5*(3 - 2*x - 3*x^2) / ((1 - x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - x^2 - x^3)).
a(n) = 2*a(n-1) + 3*a(n-2) - 6*a(n-3) - 4*a(n-4) + 5*a(n-5) + 5*a(n-6) - 2*a(n-7) - 2*a(n-8) for n>7.
(End)
From G. C. Greubel, Mar 11 2020: (Start)
a(n) = 2*(2 + Fibonacci(n+2) - 2^floor(n/2) - A084338(n+2)).
a(n) = 2*(2 + Fibonacci(n+2) - 2^floor(n/2) - b(n+7) - b(n+5)), where b(n) = A000931(n). (End)

A276275 Padovan like sequence: a(n) = a(n-2) + a(n-3) for n>3, a(1)=2, a(2)=2, a(3)=0.

Original entry on oeis.org

2, 2, 0, 4, 2, 4, 6, 6, 10, 12, 16, 22, 28, 38, 50, 66, 88, 116, 154, 204, 270, 358, 474, 628, 832, 1102, 1460, 1934, 2562, 3394, 4496, 5956, 7890, 10452, 13846, 18342, 24298, 32188, 42640, 56486, 74828, 99126, 131314, 173954, 230440, 305268, 404394, 535708

Offset: 1

Nicolas Bègue, Aug 26 2016

Obtained from Padovan Spiral number (A134816) modulo 3 reduction periodic sequence 1112201210010, 111 112 122 220 ... fourth initialization values 220, it satisfies the same recurrence a(n) = a(n-2) + a(n-3).

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

Cf. A134816, A084338.

RecurrenceTable[{a[n] == a[n - 2] + a[n - 3], a[1] == 2, a[2] == 2, a[3] == 0}, a, {n, 1, 48}] (* or *) CoefficientList[Series[2 x (1 + x - x^2)/(1 - x^2 - x^3), {x, 0, 47}], x] (* Michael De Vlieger, Sep 02 2016 *)
LinearRecurrence[{0,1,1},{2,2,0},60] (* Harvey P. Dale, Jan 27 2023 *)

G.f.: 2*x*(1 + x - x^2)/(1 - x^2 - x^3).
a(n) = A134816(n) + A007307(n-3) for n>=4.
a(n) = 2*A084338(n-3) for n>=4.

A276477 a(n) = a(n-2) + a(n-3) for n >= 3, with a(0) = a(1) = 2, a(2) = 1.

Original entry on oeis.org

2, 2, 1, 4, 3, 5, 7, 8, 12, 15, 20, 27, 35, 47, 62, 82, 109, 144, 191, 253, 335, 444, 588, 779, 1032, 1367, 1811, 2399, 3178, 4210, 5577, 7388, 9787, 12965, 17175, 22752, 30140, 39927, 52892, 70067, 92819, 122959, 162886, 215778, 285845, 378664, 501623, 664509

Offset: 0

Nicolas Bègue, Sep 04 2016

Padovan-like sequence linked to Perrin sequence.

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

Cf. A001608, A084338.

I:=[2,2,1]; [n le 3 select I[n] else Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Sep 10 2016

RecurrenceTable[{a[n] == a[n - 2] + a[n - 3], a[1] == a[2] == 2, a[3] == 1}, a, {n, 42}]
CoefficientList[Series[(x^2 - 2 x - 2)/(x^3 + x^2 - 1), {x, 0, 41}], x] (* Michael De Vlieger, Sep 06 2016 *)
LinearRecurrence[{0, 1, 1}, {2, 2, 1}, 60] (* Vincenzo Librandi, Sep 10 2016 *)

x='x+O('x^99); Vec((x^2-2*x-2)/(x^3+x^2-1)) \\ Altug Alkan, Sep 10 2016

a(n) = A001608(n) + A084338(n-7).

G.f.: (x^2-2*x-2)/(x^3+x^2-1).

cp's OEIS Frontend

A007829 From random walks on complete directed triangle.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

Sage

Formula

A276275 Padovan like sequence: a(n) = a(n-2) + a(n-3) for n>3, a(1)=2, a(2)=2, a(3)=0.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A276477 a(n) = a(n-2) + a(n-3) for n >= 3, with a(0) = a(1) = 2, a(2) = 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula