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A058809 The sequence lambda(3,n), where lambda is defined in A055203. Number of ways of placing n identifiable positive intervals with a total of exactly three starting and/or finishing points. 6
0, 0, 6, 24, 78, 240, 726, 2184, 6558, 19680, 59046, 177144, 531438, 1594320, 4782966, 14348904, 43046718, 129140160, 387420486, 1162261464, 3486784398, 10460353200, 31381059606, 94143178824, 282429536478, 847288609440 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For all n, a(n)=1*3^n-3*1^n+3*0^n-1*0^n [with 0^0=1] where powers are taken of triangular numbers and multiplied by binomial coefficients with alternating signs.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4, -3).

FORMULA

For n>0, a(n) = 3^n-3 = 3*a(n-1)+6.

a(0)=0, a(1)=0, a(2)=6, a(n)=4*a(n-1)-3*a(n-2). - Harvey P. Dale, Sep 29 2013

EXAMPLE

a(2)=6 since intervals a-a and b-b can be combined as a-ab-b, a-b-ab, ab-a-b, b-ab-a, b-a-ab, or ab-b-a.

MATHEMATICA

Join[{0}, NestList[3#+6&, 0, 30]] (* or *) Join[{0}, LinearRecurrence[{4, -3}, {0, 6}, 30]] (* Harvey P. Dale, Sep 29 2013 *)

CROSSREFS

Cf. A059116, A059117.

Sequence in context: A276179 A162583 A259662 * A140088 A011855 A173031

Adjacent sequences:  A058806 A058807 A058808 * A058810 A058811 A058812

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jan 03 2001

EXTENSIONS

Additional comments from Henry Bottomley, Jan 05 2001

STATUS

approved

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Last modified October 16 20:35 EDT 2019. Contains 328103 sequences. (Running on oeis4.)