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A059517
The sequence A059515(3,n). Number of ways of placing n identifiable nonnegative intervals with a total of exactly three starting and/or finishing points.
0
0, 0, 12, 138, 1056, 7050, 44472, 273378, 1659936, 10018650, 60289032, 362265618, 2175188016, 13055911050, 78349815192, 470141937858, 2820980767296, 16926272024250, 101558794406952, 609356253226098, 3656147979709776, 21936919259318250, 131621609699088312
OFFSET
0,3
FORMULA
a(n) = A058809(n)+A059116(n) = 6^n-3*3^n+3 (for n>0).
a(n) = 10*a(n-1)-27*a(n-2)+18*a(n-3) for n>3. - Colin Barker, Sep 13 2014
G.f.: -6*x^2*(3*x+2) / ((x-1)*(3*x-1)*(6*x-1)). - Colin Barker, Sep 13 2014
EXAMPLE
a(2)=12 since if aA indicates a zero length interval and a-A one of positive length the possibilities are: aA-b-B, b-aA-B, b-B-aA, bB-a-A, a-bB-A, a-A-bB, ab-A-B, ab-B-A, a-b-AB, b-a-AB, a-bA-B, b-a-AB.
PROG
(PARI) concat([0, 0], Vec(-6*x^2*(3*x+2)/((x-1)*(3*x-1)*(6*x-1)) + O(x^100))) \\ Colin Barker, Sep 13 2014
CROSSREFS
Cf. A059516.
Sequence in context: A264503 A000467 A372733 * A243966 A377260 A377234
KEYWORD
nonn,easy
AUTHOR
Henry Bottomley, Jan 19 2001
EXTENSIONS
More terms from Colin Barker, Sep 13 2014
STATUS
approved