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A289143 Matching number of the n-triangular honeycomb acute knight graph. 3
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 May 7 11:32 EDT 2021. Contains 343650 sequences. (Running on oeis4.)