login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A192742 Number of matchings in the n-antiprism graph. 4
3, 15, 51, 191, 708, 2631, 9775, 36319, 134943, 501380, 1862875, 6921503, 25716811, 95550687, 355018116, 1319068095, 4900991135, 18209608887, 67657713855, 251381908996, 934008268531, 3470303209839, 12893894812259, 47907203888767, 177998984624708, 661354367518327, 2457258957728079, 9129933787225743, 33922224882718431, 126037862684586116 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Antiprism graphs have n >= 3; sequence extended via recurrence to start at n = 1

LINKS

Table of n, a(n) for n=1..30.

Eric Weisstein's World of Mathematics, Antiprism Graph

Eric Weisstein's World of Mathematics, Independent Edge Set

Eric Weisstein's World of Mathematics, Matching

Index entries for linear recurrences with constant coefficients, signature (3,3,-1,-1).

FORMULA

a(n) = 3*a(n-1) + 3*a(n-2) - a(n-3) - a(n-4).

G.f.: -x*(-3-6*x+3*x^2+4*x^3)/(1-3*x-3*x^2+x^3+x^4).

a(n) = A073817(2*n). - Greg Dresden, Jan 27 2021

MATHEMATICA

LinearRecurrence[{3, 3, -1, -1}, {3, 15, 51, 191}, 20]

Table[RootSum[1 + # - 3 #^2 - 3 #^3 + #^4 &, #^n &], {n, 20}]

CoefficientList[Series[(3 + 6 x - 3 x^2 - 4 x^3)/(1 - 3 x - 3 x^2 + x^3 + x^4), {x, 0, 20}], x]

CROSSREFS

Bisection of A073817.

Sequence in context: A282464 A284663 A231747 * A166035 A038192 A212869

Adjacent sequences:  A192739 A192740 A192741 * A192743 A192744 A192745

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Jul 09 2011

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 22 09:44 EDT 2021. Contains 348160 sequences. (Running on oeis4.)