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A290700 Number of minimal edge covers in the n-prism graph. 1
1, 5, 25, 49, 141, 389, 1009, 2761, 7441, 19925, 53769, 144721, 389325, 1048325, 2821665, 7594761, 20444065, 55029413, 148124153, 398713969, 1073231821, 2888859781, 7776063377, 20931130057, 56341150641, 151655712629, 408217654249, 1098815597201 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The n-prism graph is well defined for n >= 3. Sequence extended to n = 1 using recurrence. - Andrew Howroyd, Aug 10 2017
LINKS
Eric Weisstein's World of Mathematics, Minimal Edge Cover
Eric Weisstein's World of Mathematics, Prism Graph
Index entries for linear recurrences with constant coefficients, signature (1, 2, 6, 2, 2, -2, -2, -1, 1).
FORMULA
From Andrew Howroyd, Aug 10 2017: (Start)
a(n) = a(n-1) + 2*a(n-2) + 6*a(n-3) + 2*a(n-4) + 2*a(n-5) - 2*a(n-6) - 2*a(n-7) - a(n-8) + a(n-9) for n > 9.
G.f.: x*(1 + 4*x + 18*x^2 + 8*x^3 + 10*x^4 - 12*x^5 - 14*x^6 - 8*x^7 + 9*x^8)/((1 - 2*x - 2*x^2 + x^4)*(1 + x + x^2 - x^3)*(1 + x^2)).
(End)
MATHEMATICA
Table[2 Cos[n Pi/2] + RootSum[-1 + # + #^2 + #^3 &, #^n &] -
RootSum[1 - 2 #^2 - 2 #^3 + #^4 &, -2 #^(n + 2) - 2 #^(n + 3) + #^(n + 4) &], {n, 20}]
LinearRecurrence[{1, 2, 6, 2, 2, -2, -2, -1, 1}, {1, 5, 25, 49, 141, 389, 1009, 2761, 7441}, 20]
CoefficientList[Series[-( (1 + 4 x + 18 x^2 + 8 x^3 + 10 x^4 - 12 x^5 - 14 x^6 - 8 x^7 + 9 x^8)/((1 + x^2) (-1 - x - x^2 + x^3) (1 - 2 x - 2 x^2 + x^4))), {x, 0, 20}], x]
PROG
(PARI)
Vec((1 + 4*x + 18*x^2 + 8*x^3 + 10*x^4 - 12*x^5 - 14*x^6 - 8*x^7 + 9*x^8)/((1 - 2*x - 2*x^2 + x^4)*(1 + x + x^2 - x^3)*(1 + x^2))+O(x^30)) \\ Andrew Howroyd, Aug 10 2017
CROSSREFS
Cf. A123304.
Sequence in context: A298041 A074493 A262760 * A136914 A136913 A136911
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Aug 09 2017
EXTENSIONS
a(1)-a(2) and terms a(9) and beyond from Andrew Howroyd, Aug 10 2017
STATUS
approved

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Last modified April 20 00:26 EDT 2024. Contains 371798 sequences. (Running on oeis4.)