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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jun 26 2017
STATUS
approved