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A060561
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Number of ways to color vertices of a 9-gon using <= n colors, allowing rotations and reflections.
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1
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0, 1, 46, 1219, 15084, 110085, 563786, 2250311, 7472984, 21552969, 55605670, 131077771, 286779076, 589324749, 1148105154, 2136122255, 3818273456, 6588925841, 11020906014, 17928333139, 28446045340, 44128712341, 67073090106
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,500
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FORMULA
| (n^9+9*n^5+2*n^3+6*n)/18.
a(0)=0, a(1)=1, a(2)=46, a(3)=1219, a(4)=15084, a(5)=110085, a(6)=563786, a(7)=2250311, a(8)=7472984, a(9)=21552969, a(n)=10*a(n-1)-45*a(n-2)+ 120*a(n-3)-210*a(n-4)+252*a(n-5)-210*a(n-6)+120*a(n-7)-45*a(n-8)+ 10*a(n-9)-a(n-10) [From Harvey P. Dale, Nov 23 2011]
G.f.: x*(1+36*x+804*x^2+4844*x^3+8790*x^4+4844*x^5+804*x^6+36*x^7+x^8)/(1-x)^10. [Colin Barker, Jan 29 2012]
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MATHEMATICA
| Table[(n^9+9n^5+2n^3+6*n)/18, {n, 0, 30}] (* or *) LinearRecurrence[ {10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 1, 46, 1219, 15084, 110085, 563786, 2250311, 7472984, 21552969}, 30] (* From Harvey P. Dale, Nov 23 2011 *)
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PROG
| (PARI) { for (n=0, 500, write("b060561.txt", n, " ", (n^9 + 9*n^5 + 2*n^3 + 6*n)/18); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 07 2009]
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CROSSREFS
| Sequence in context: A162452 A010998 A004424 * A188412 A066403 A028574
Adjacent sequences: A060558 A060559 A060560 * A060562 A060563 A060564
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Apr 12 2001
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