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A298822 Number of minimum edge covers in the n-dipyramidal graph. 3
1, 2, 21, 8, 85, 18, 217, 32, 441, 50, 781, 72, 1261, 98, 1905, 128, 2737, 162, 3781, 200, 5061, 242, 6601, 288, 8425, 338, 10557, 392, 13021, 450, 15841, 512, 19041, 578, 22645, 648, 26677, 722, 31161, 800, 36121, 882, 41581, 968, 47565, 1058, 54097, 1152 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The size of a minimum edge cover is given by floor((n + 3)/2). - Andrew Howroyd, Jun 26 2018

LINKS

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

Eric Weisstein's World of Mathematics, Dipyramidal Graph

Eric Weisstein's World of Mathematics, Minimum Edge Cover

Index entries for linear recurrences with constant coefficients, signature (0, 4, 0, -6, 0, 4, 0, -1).

FORMULA

From Andrew Howroyd, Jun 26 2018: (Start)

a(2*n) = 2*n^2, a(2*n-1) = (2*n-1)*(2*n^2 - 1).

a(n) = 4*a(n-2) - 6*a(n-4) + 4*a(n-6) - a(n-8) for n > 8.

G.f.: x*(1 + 2*x + 17*x^2 + 7*x^4 - 2*x^5 - x^6)/((1 - x)^4*(1 + x)^4). (End)

a(n) = n*(n^2 + 3*n - 1 - (-1)^n*(n^2 + n - 1))/4. - Eric W. Weisstein, Jun 27 2018

MATHEMATICA

Table[n (n^2 + 3 n - 1 - (-1)^n (n^2 + n - 1))/4, {n, 20}]

LinearRecurrence[{0, 4, 0, -6, 0, 4, 0, -1}, {1, 2, 21, 8, 85, 18, 217, 32}, 20]

CoefficientList[Series[(1 + 2 x + 17 x^2 + 7 x^4 - 2 x^5 - x^6)/(-1 + x^2)^4, {x, 0, 20}], x]

PROG

(PARI) a(n)={n*if(n%2, 2*(n\2+1)^2-1, n\2)} \\ Andrew Howroyd, Jun 26 2018

CROSSREFS

Cf. A296995, A297713.

Sequence in context: A024230 A105666 A058261 * A072397 A077208 A321534

Adjacent sequences:  A298819 A298820 A298821 * A298823 A298824 A298825

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Jun 18 2018

EXTENSIONS

a(1)-a(2) and terms a(10) and beyond from Andrew Howroyd, Jun 26 2018

STATUS

approved

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Last modified July 23 12:06 EDT 2021. Contains 346259 sequences. (Running on oeis4.)