

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
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OFFSET

0,3


LINKS

Table of n, a(n) for n=0..22.
IBM Ponder This, Jan 01 2001
Index entries for linear recurrences with constant coefficients, signature (10,27,18).


FORMULA

a(n) = A058809(n)+A059116(n) = 6^n3*3^n+3 (for n>0).
a(n) = 10*a(n1)27*a(n2)+18*a(n3) for n>3.  Colin Barker, Sep 13 2014
G.f.: 6*x^2*(3*x+2) / ((x1)*(3*x1)*(6*x1)).  Colin Barker, Sep 13 2014


EXAMPLE

a(2)=12 since if aA indicates a zero length interval and aA one of positive length the possibilities are: aAbB, baAB, bBaA, bBaA, abBA, aAbB, abAB, abBA, abAB, baAB, abAB, baAB.


PROG

(PARI) concat([0, 0], Vec(6*x^2*(3*x+2)/((x1)*(3*x1)*(6*x1)) + O(x^100))) \\ Colin Barker, Sep 13 2014


CROSSREFS

Cf. A059516.
Sequence in context: A216081 A264503 A000467 * A243966 A097167 A125469
Adjacent sequences: A059514 A059515 A059516 * A059518 A059519 A059520


KEYWORD

nonn,easy


AUTHOR

Henry Bottomley, Jan 19 2001


EXTENSIONS

More terms from Colin Barker, Sep 13 2014


STATUS

approved



