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A289143
Matching number of the n-triangular honeycomb acute knight graph.
4
0, 0, 3, 3, 6, 9, 12, 18, 21, 27, 33, 39, 45, 51, 60, 67, 75, 84, 94, 105, 114, 126, 138, 150, 162, 174, 189, 202, 216, 231, 247, 264, 279, 297, 315, 333, 351, 369, 390, 409, 429, 450, 472, 495, 516, 540, 564, 588, 612, 636, 663, 688, 714, 741, 769, 798, 825, 855, 885, 915, 945, 975, 1008, 1039, 1071, 1104, 1138, 1173, 1206, 1242, 1278, 1314
OFFSET
1,3
LINKS
Eric Weisstein's World of Mathematics, Matching
Eric Weisstein's World of Mathematics, Matching Number
Eric Weisstein's World of Mathematics, Maximum Independent Edge Set
FORMULA
For n > 13, a(n) = (n^2-n+6-2*a(n-6))/2.
From Colin Barker, Jun 26 2017: (Start)
G.f.: x^3*(3 - 6*x + 6*x^2 - 3*x^3 + 3*x^5 - 3*x^6 + 3*x^8 - 3*x^9 + 3*x^11 - 3*x^12 + x^13) / ((1 - x)^3*(1 + x^2)*(1 - x^2 + x^4)).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) - a(n-6) + 3*a(n-7) - 3*a(n-8) + a(n-9) for n>9.
(End)
MATHEMATICA
Table[Piecewise[{{3, n == 4}, {12, n == 7}}, (3 (n^2 + n - 3) + 5 Cos[n Pi/2] + 4 (-1)^n (Cos[n Pi/3] + Sqrt[3] Sin[n Pi/3]) (Cos[n Pi/2] - Sin[n Pi/2]) - 5 Sin[n Pi/2])/12], {n, 50}]
PROG
(PARI) concat(vector(2), Vec( x^3*(3 - 6*x + 6*x^2 - 3*x^3 + 3*x^5 - 3*x^6 + 3*x^8 - 3*x^9 + 3*x^11 - 3*x^12 + x^13) / ((1 - x)^3*(1 + x^2)*(1 - x^2 + x^4)) + O(x^80))) \\ Colin Barker, Jun 26 2017
CROSSREFS
Sequence in context: A098358 A136289 A128012 * A323451 A280240 A058628
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jun 26 2017
STATUS
approved