A200752 -id:A200752 - cp's OEIS frontend

A202207 a(n) = 3*a(n-1) - a(n-2) + a(n-3) with a(0)=1, a(1)=2, a(2)=5.

1, 2, 5, 14, 39, 108, 299, 828, 2293, 6350, 17585, 48698, 134859, 373464, 1034231, 2864088, 7931497, 21964634, 60826493, 168446342, 466477167, 1291811652, 3577404131, 9906877908, 27435041245, 75975649958, 210398786537

Offset: 0

Philippe Deléham, Dec 14 2011

Index entries for linear recurrences with constant coefficients, signature (3,-1,1).

Cf. A200752.

my(x='x+O('x^40)); Vec((1-x)/(1-3*x+x^2-x^3)) \\ Michel Marcus, Apr 10 2024

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

a(n) = A200752(n+3) - A200752(n+2). - R. J. Mathar, Dec 15 2011

A289666 a(n) = number of weakly threshold graphs on n nodes.

Original entry on oeis.org

0, 1, 2, 4, 9, 21, 52, 134, 355, 957, 2608, 7154, 19701, 54379, 150302, 415762, 1150609, 3185147, 8818620, 24418128, 67615743, 187239359, 518506932, 1435875288, 3976322869, 11011542937, 30494088494, 84446895364, 233857897749, 647620493541

Offset: 0

N. J. A. Sloane, Jul 25 2017

Colin Barker, Table of n, a(n) for n = 0..1000
Michael D. Barrus, Weakly threshold graphs, arXiv preprint arXiv:1608.01358 [math.CO], 2016. See W(x).
Index entries for linear recurrences with constant coefficients, signature (4,-3,-1,0,-1).

a = DifferenceRoot[Function[{a, n}, {a[n] + a[n+2] + 3a[n+3] - 4a[n+4] + a[n+5] == 0, a[0]==0, a[1]==1, a[2]==2, a[3]==4, a[4]==9, a[5]==21}]];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jan 09 2019 *)
LinearRecurrence[{4,-3,-1,0,-1},{0,1,2,4,9,21},30] (* Harvey P. Dale, Sep 15 2024 *)

concat(0, Vec(x*(1 - 2*x - x^2 - x^4) / ((1 - x - x^2)*(1 - 3*x + x^2 - x^3)) + O(x^30))) \\ Colin Barker, Jul 26 2017

G.f.: -(x^4+x^2+2*x-1)*x/((x^2+x-1)*(x^3-x^2+3*x-1)).
a(n) = 4*a(n-1) - 3*a(n-2) - a(n-3) - a(n-5) for n>5. - Colin Barker, Jul 26 2017
3*a(n) = 2*A000045(n+1) + A200752(n+3) -2*A200752(n+2), n>0. - R. J. Mathar, Aug 05 2017

cp's OEIS Frontend

A202207 a(n) = 3*a(n-1) - a(n-2) + a(n-3) with a(0)=1, a(1)=2, a(2)=5.

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