A050400 Number of independent sets of vertices in P_3 X C_n (n > 2).

5, 1, 17, 43, 181, 621, 2309, 8303, 30277, 109753, 398857, 1447931, 5258725, 19095285, 69344061, 251811903, 914429445, 3320635025, 12058502657, 43789003563, 159014593621, 577442573597, 2096914206261, 7614694850543, 27651860345029, 100414447219721, 364643142303353

Offset: 0

Author

Stephen G Penrice, Dec 21 1999

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,8,6,-1,-1).

Crossrefs

Column 3 of A286513.

Programs

GAP

a:=[5,1,17,43,181];; for n in [6..30] do a[n]:=a[n-1]+8*a[n-2] +6*a[n-3] -a[n-4]-a[n-5]; od; a; # G. C. Greubel, Oct 30 2019

Magma

I:=[5,1,17,43,181]; [n le 5 select I[n] else Self(n-1) + 8*Self(n-2) + 6*Self(n-3) - Self(n-4) - Self(n-5): n in [1..30]]; // Vincenzo Librandi, May 11 2017

Maple

seq(coeff(series((5-4*x-24*x^2-12*x^3+x^4)/((1+x)*(1-2*x-6*x^2+x^4)), x, n+1), x, n), n = 0..30); # G. C. Greubel, Oct 30 2019

Mathematica

CoefficientList[Series[(5-4*x-24*x^2-12*x^3+x^4)/((1+x)*(1-2*x-6*x^2+ x^4)), {x, 0, 30}], x] (* Vincenzo Librandi, May 11 2017 *)

PARI

my(x='x+O('x^30)); Vec((5-4*x-24*x^2-12*x^3+x^4)/((1+x)*(1-2*x-6*x^2+x^4))) \\ G. C. Greubel, Oct 30 2019

Sage

def A077952_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((5-4*x-24*x^2-12*x^3+x^4)/((1+x)*(1-2*x-6*x^2+x^4))).list()
A077952_list(30) # G. C. Greubel, Oct 30 2019

Formula

a(n) = a(n-1) + 8*a(n-2) + 6*a(n-3) - a(n-4) - a(n-5).

G.f.: (5-4*x-24*x^2-12*x^3+x^4)/((1+x)*(1-2*x-6*x^2+x^4)). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009

Extensions

More terms from Michael Lugo (mlugo(AT)thelabelguy.com), Dec 22 1999