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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Colin Barker, Table of n, a(n) for n = 1..1000 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 Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,-1,3,-3,1). 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 Adjacent sequences: A289140 A289141 A289142 * A289144 A289145 A289146 KEYWORD nonn,easy AUTHOR Eric W. Weisstein, Jun 26 2017 STATUS approved

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Last modified December 3 18:52 EST 2023. Contains 367540 sequences. (Running on oeis4.)