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A297064
Number of maximal matchings in the n-dipyramidal graph.
1
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
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
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jun 18 2018
STATUS
approved