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A060888
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n^6-n^5+n^4-n^3+n^2-n+1.
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22
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1, 1, 43, 547, 3277, 13021, 39991, 102943, 233017, 478297, 909091, 1623931, 2756293, 4482037, 7027567, 10678711, 15790321, 22796593, 32222107, 44693587, 60952381, 81867661, 108450343, 141867727, 183458857, 234750601, 297474451
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OFFSET
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0,3
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COMMENTS
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Number of walks of length 7 between any two distinct nodes of the complete graph K_{n+1} (n>=1). - Emeric Deutsch, Apr 01 2004
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,1000
Index to sequences with linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
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FORMULA
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G.f.=(1-6x+57x^2+232x^3+351x^4+78x^5+7x^6)/(1-x)^7. - Emeric Deutsch, Apr 01 2004
a(0)=1, a(1)=1, a(2)=43, a(3)=547, a(4)=3277, a(5)=13021, a(6)=39991, 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) -- From Harvey P. Dale, Jul 21 2012
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MATHEMATICA
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Table[1-n+n^2-n^3+n^4-n^5+n^6, {n, 0, 30}] (* or *) LinearRecurrence[ {7, -21, 35, -35, 21, -7, 1}, {1, 1, 43, 547, 3277, 13021, 39991}, 30] (* or *) Cyclotomic[14, Range[0, 30]] (* Harvey P. Dale, Jul 21 2012 *)
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PROG
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(PARI) { for (n=0, 1000, write("b060888.txt", n, " ", n^6 - n^5 + n^4 - n^3 + n^2 - n + 1); ) } [From Harry J. Smith, Jul 14 2009]
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CROSSREFS
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Let Phi_k(x) be the k-th cyclotomic polynomial and form the sequence Phi_k(0), Phi_k(1), Phi_k(2), ... This gives A000027 (k=2), A002061 (k=3), A002522 (k=4), A053699 (k=5), A002061 (k=6), A053716 (k=7), A002523 (k=8), A060883 (k=9), A060884 (k=10), A060885 (k=11), A060886 (k=12), A060887 (k=13), A060888 (k=14), A060889 (k=15), A060890 (k=16), A060891 (k=18), A060892 (k=20), A060893 (k=24), A060894 (k=30), A060895 (k=32), A060896 (k=36).
Sequence in context: A184153 A184145 A008388 * A146979 A157722 A010959
Adjacent sequences: A060885 A060886 A060887 * A060889 A060890 A060891
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, May 05 2001
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STATUS
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approved
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