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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

Andrew Howroyd, Table of n, a(n) for n = 1..200

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

Adjacent sequences:  A290697 A290698 A290699 * A290701 A290702 A290703

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 July 5 14:33 EDT 2020. Contains 335472 sequences. (Running on oeis4.)