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A050402 Number of independent sets of nodes in C_4 X C_n (n > 2). 1
7, 1, 35, 121, 743, 3561, 18995, 96433, 500871, 2573905, 13292995, 68492073, 353290343, 1821383097, 9392360019, 48428332641, 249716406791, 1287608913057, 6639354593123, 34234612471001, 176524935990503, 910219628918665, 4693389213891699, 24200638961917201 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
C. Bautista-Ramos and C. Guillen-Galvan, Fibonacci numbers of generalized Zykov sums, J. Integer Seq., 15 (2012), Article 12.7.8
Eric Weisstein's World of Mathematics, Independent Vertex Set
Eric Weisstein's World of Mathematics, Torus Grid Graph
FORMULA
a(n) = a(n-1) + 17*a(n-2) + 23*a(n-3) + a(n-4) - 9*a(n-5) - a(n-6) + a(n-7).
G.f.: (7 -13*x -72*x^2 -20*x^3 +17*x^4 +x^5)/((1+x)*(1+2*x-x^2)*(1-5*x-x^2+x^3)). - Colin Barker, Aug 31 2012
MAPLE
seq(coeff(series((7-13*x-72*x^2-20*x^3+17*x^4+x^5)/((1+x)*(1+2*x-x^2) *(1-5*x-x^2+x^3)), x, n+1), x, n), n = 0 ..30); # G. C. Greubel, Oct 30 2019
MATHEMATICA
CoefficientList[Series[(7 -13*x -72*x^2 -20*x^3 +17*x^4 +x^5)/((1+x)*(1+2*x-x^2)*(1-5*x-x^2+x^3)), {x, 0, 30}], x]
PROG
(PARI) Vec((7-13*x-72*x^2-20*x^3+17*x^4+x^5)/((1+x)*(1+2*x-x^2)*(1-5*x- x^2+x^3)) + O(x^30)) \\ Colin Barker, May 11 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (7 -13*x -72*x^2 -20*x^3 +17*x^4 +x^5)/((1+x)*(1+2*x-x^2)*(1-5*x-x^2+x^3)) )); // G. C. Greubel, Oct 30 2019
(Sage)
def A050402_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P((7 -13*x -72*x^2 -20*x^3 +17*x^4 +x^5)/((1+x)*(1+2*x-x^2)*(1-5*x-x^2+x^3))).list()
A050402_list(30) # G. C. Greubel, Oct 30 2019
(GAP) a:=[7, 1, 35, 121, 743, 3561];; for n in [7..30] do a[n]:=2*a[n-1] +15*a[n-2]+8*a[n-3]-7*a[n-4]-2*a[n-5]-a[n-6]; od; a; # G. C. Greubel, Oct 30 2019
CROSSREFS
Sequence in context: A002678 A147482 A171770 * A027643 A373036 A225122
KEYWORD
easy,nonn
AUTHOR
Stephen G Penrice, Dec 21 1999
EXTENSIONS
More terms from Michael Lugo (mlugo(AT)thelabelguy.com), Dec 22 1999
STATUS
approved

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Last modified June 17 11:15 EDT 2024. Contains 373445 sequences. (Running on oeis4.)