A351586 Number of minimal edge covers of the 2n-crossed prism graph.

5, 49, 425, 3137, 22985, 172081, 1284953, 9579841, 71450345, 532960209, 3975244025, 29650441313, 221157005321, 1649567697393, 12303803776025, 91771679496321, 684507131648297, 5105605684127761, 38081720625979193, 284044154060630177, 2118630149395512905, 15802450588258380337

Offset

1,1

Comments

The 2n-crossed prism graph is well-defined for n >= 2. The sequence has been extrapolated to a(1) using the recurrence. - Andrew Howroyd, Feb 21 2022

Links

Table of n, a(n) for n=1..22.

Eric Weisstein's World of Mathematics, Crossed Prism Graph

Eric Weisstein's World of Mathematics, Minimal Edge Cover

Index entries for linear recurrences with constant coefficients, signature (5,12,40,56,-8,-32).

Formula

From Andrew Howroyd, Feb 21 2022: (Start)

a(n) = 5*a(n-1) + 12*a(n-2) + 40*a(n-3) + 56*a(n-4) - 8*a(n-5) - 32*a(n-6) for n > 6.

G.f.: x*(5 + 24*x + 120*x^2 + 224*x^3 - 40*x^4 - 192*x^5)/(1 - 5*x - 12*x^2 - 40*x^3 - 56*x^4 + 8*x^5 + 32*x^6).

(End)

Mathematica

LinearRecurrence[{5, 12, 40, 56, -8, -32}, {5, 49, 425, 3137, 22985, 172081}, 20]
Table[RootSum[32 + 8 # - 56 #^2 - 40 #^3 - 12 #^4 - 5 #^5 + #^6 &, #^n &], {n, 20}]
CoefficientList[Series[(5 + 24 x + 120 x^2 + 224 x^3 - 40 x^4 - 192 x^5)/(1 - 5 x - 12 x^2 - 40 x^3 - 56 x^4 + 8 x^5 + 32 x^6), {x, 0, 20}], x]

Prog

(PARI) Vec((5 + 24*x + 120*x^2 + 224*x^3 - 40*x^4 - 192*x^5)/(1 - 5*x - 12*x^2 - 40*x^3 - 56*x^4 + 8*x^5 + 32*x^6) + O(x^20)) \\ Andrew Howroyd, Feb 21 2022

Crossrefs

Cf. A297028, A297476.

Sequence in context: A093188 A218421 A293841 * A224756 A198969 A155629

Adjacent sequences: A351583 A351584 A351585 * A351587 A351588 A351589

Keyword

nonn,easy

Author

Eric W. Weisstein, Feb 14 2022

Extensions

a(1) and terms a(5) and beyond from Andrew Howroyd, Feb 21 2022

Status

approved