The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A182788 Number of n-colorings of the Triangle Graph of order 3. 12
 0, 0, 0, 6, 192, 1620, 7680, 26250, 72576, 172872, 368640, 721710, 1320000, 2283996, 3773952, 5997810, 9219840, 13770000, 20054016, 28564182, 39890880, 54734820, 73920000, 98407386, 129309312, 167904600, 215654400, 274218750, 345473856 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The Triangle Graph of order 3 has 3 rows with k vertices in row k. Each vertex is connected to the neighbors in the same row and up to two vertices in each of the neighboring rows. The Graph has 6 vertices and 9 edges altogether. REFERENCES Burkard Polster and Marty Ross, Math Goes to the Movies, The Johns Hopkins University Press, Baltimore, 2013, §1.10 Mathematics: Graph Theory 3, pp. 16-17. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Triangle Graph Wikipedia, Chromatic polynomial Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1). FORMULA a(n) = n*(n-1)*(n-2)^4. G.f.: 6*x^3*(1 + 25*x + 67*x^2 + 27*x^3) / (1-x)^7. a(0)=0, a(1)=0, a(2)=0, a(3)=6, a(4)=192, a(5)=1620, a(6)=7680, a(n) = 7*a(n-1) -21*a(n-2) +35*a(n-3) -35*a(n-4) +21*a(n-5) -7*a(n-6) +a(n-7). - Harvey P. Dale, Dec 10 2011 MAPLE a:= n-> n*(n-1)*(n-2)^4: seq(a(n), n=0..30); MATHEMATICA Table[n(n-1)(n-2)^4, {n, 0, 30}] (* or *) LinearRecurrence[ {7, -21, 35, -35, 21, -7, 1}, {0, 0, 0, 6, 192, 1620, 7680}, 30] (* Harvey P. Dale, Dec 10 2011 *) PROG (PARI) a(n)=n*(n-1)*(n-2)^4 \\ Charles R Greathouse IV, Jun 22 2016 CROSSREFS 3rd column of A182797. Cf. A178435, A182798, A182789, A182790, A182791, A182792, A182793, A182794, A182795, A182796. Sequence in context: A222016 A059491 A024279 * A232214 A012205 A156122 Adjacent sequences:  A182785 A182786 A182787 * A182789 A182790 A182791 KEYWORD nonn,easy AUTHOR Alois P. Heinz, Dec 02 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 1 16:44 EST 2021. Contains 349430 sequences. (Running on oeis4.)