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, 12, 138, 1056, 7050, 44472, 273378, 1659936, 10018650, 60289032, 362265618, 2175188016, 13055911050, 78349815192, 470141937858, 2820980767296, 16926272024250, 101558794406952, 609356253226098, 3656147979709776, 21936919259318250, 131621609699088312

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