login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
Eric Weisstein's World of Mathematics, Dipyramidal Graph
Eric Weisstein's World of Mathematics, Minimum Edge Cover
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
Sequence in context: A358520 A105666 A058261 * A072397 A077208 A321534
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 22 11:27 EDT 2024. Contains 373570 sequences. (Running on oeis4.)