A297064 Number of maximal matchings in the n-dipyramidal graph.

2, 4, 12, 14, 40, 56, 112, 178, 306, 482, 792, 1214, 1924, 2914, 4470, 6706, 10064, 14924, 22078, 32382, 47376, 68862, 99820, 144002, 207150, 296896, 424386, 604802, 859850, 1219352, 1725460, 2436322, 3433452, 4829532, 6781600, 9506810, 13306606, 18597506, 25956060, 36177962

Offset

1,1

Comments

Extended to a(1) using the recurrence.

Links

Table of n, a(n) for n=1..40.

Eric Weisstein's World of Mathematics, Dipyramidal Graph

Eric Weisstein's World of Mathematics, Matching

Eric Weisstein's World of Mathematics, Maximal Independent Edge Set

Index entries for linear recurrences with constant coefficients, signature (0, 5, 3, -10, -12, 7, 18, 4, -11, -8, 1, 3, 1).

Formula

a(n) = 5*a(n-2) + 3*a(n-3) - 10*a(n-4) - 12*a(n-5) + 7*a(n-6) + 18*a(n-7) + 4*a(n-8) - 11*a(n-9) - 8*a(n-10) + a(n-11) + 3*a(n-12) + a(n-13).

G.f.: -2*(1 + 2*x + x^2 - 6*x^3 - 6*x^4 + 7*x^5 + 12*x^6 - x^7 - 9*x^8 - 6 x^9 + 2 x^11 + x^12)/((-1 + x^2)^2*(-1 + x^2 + x^3)^3).

Mathematica

LinearRecurrence[{0, 5, 3, -10, -12, 7, 18, 4, -11, -8, 1, 3, 1}, {2, 4, 12, 14, 40, 56, 112, 178, 306, 482, 792, 1214, 1924}, 20]
CoefficientList[Series[-2 (1 + 2 x + x^2 - 6 x^3 - 6 x^4 + 7 x^5 + 12 x^6 - x^7 - 9 x^8 - 6 x^9 + 2 x^11 + x^12)/((-1 + x^2)^2 (-1 + x^2 + x^3)^3), {x, 0, 20}], x]

Crossrefs

Sequence in context: A111069 A107295 A039564 * A263466 A106135 A067268

Adjacent sequences: A297061 A297062 A297063 * A297065 A297066 A297067

Keyword

nonn

Author

Eric W. Weisstein, Jun 18 2018

Status

approved