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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 (list; graph; refs; listen; history; text; internal format)
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^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: 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

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Last modified December 9 19:36 EST 2022. Contains 358703 sequences. (Running on oeis4.)