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A060884
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n^4-n^3+n^2-n+1.
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25
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1, 1, 11, 61, 205, 521, 1111, 2101, 3641, 5905, 9091, 13421, 19141, 26521, 35855, 47461, 61681, 78881, 99451, 123805, 152381, 185641, 224071, 268181, 318505, 375601, 440051, 512461, 593461, 683705, 783871, 894661, 1016801, 1151041
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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 5 between any two distinct nodes of the complete graph K_{n+1} (n>=1). Example: a(1)=1 because in the complete graph AB we have only one walk of length 5 between A and B: ABABAB. - 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 (5,-10,10,-5,1).
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FORMULA
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G.f.=(1-4x+16x^2+6x^3+5x^4)/(1-x)^5. - Emeric Deutsch, Apr 01 2004
t^4-t^3+t^2-t+1 is the Alexander polynomial (with negative powers cleared) of the cinquefoil knot (torus knot T(5,2)). The associated Seifert matrix S is [[ -1, -1, 0, -1], [ 0, -1, 0, 0], [ -1, -1, -1, -1], [ 0, -1, 0, -1]]. a(n) = det(transpose(S)-n*S). Cf. A084849. - Peter Bala, Mar 14 2012
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PROG
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(PARI) { for (n=0, 1000, write("b060884.txt", n, " ", n^4 - n^3 + n^2 - n + 1); ) } [From Harry J. Smith, Jul 13 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: A078554 A189227 A002650 * A141935 A222408 A001847
Adjacent sequences: A060881 A060882 A060883 * A060885 A060886 A060887
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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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