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A160050
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Numerator of the Harary number for the star graph s_n.
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7
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0, 1, 5, 9, 7, 10, 27, 35, 22, 27, 65, 77, 45, 52, 119, 135, 76, 85, 189, 209, 115, 126, 275, 299, 162, 175, 377, 405, 217, 232, 495, 527, 280, 297, 629, 665, 351, 370, 779, 819, 430, 451, 945, 989, 517, 540, 1127, 1175, 612, 637, 1325, 1377, 715, 742, 1539
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OFFSET
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1,3
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LINKS
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Table of n, a(n) for n=1..55.
Eric Weisstein's World of Mathematics, Harary Index
Index to sequences with linear recurrences with constant coefficients, signature (3,-6,10,-12,12,-10,6,-3,1).
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FORMULA
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Numerator of (1/4)*(n+2)*(n-1). - Joerg Arndt, Jan 04 2011
It appears that a(n + 1) = A060819(n-1) * A060819(n + 2). - Paul Curtz, Dec 23 2010 [Corrected by Joerg Arndt, Jan 04 2011]
G.f.: x^2*(-1-2*x-5*x^4+3*x^5-2*x^6+x^7) / ( (x-1)^3*(x^2+1)^3 ). - R. J. Mathar, Jan 04 2011
a(1+4*n) = (A000217(n+1)-1)/2, a(2+4*n)=(A000217(n+2)-1)/2, a(3+4*n) = A000217(n+3)-1, a(4+4*n) = A000217(n+4)-1. - Paul Curtz, Dec 23 2010.
a(n)= 3*a(n-4) -3*a(n-8) +a(n-12). This is not the shortest recurrence. -Paul Curtz, Mar 27 2011
a(1+3*n) = numerator of 9*n*(n+1)/4 = 9*A064038(1+n). - Paul Curtz, Apr 06 2011
a(n) = n*(n+3)*(3-i^(n*(n-1)))/8, where i=sqrt(-1). - Bruno Berselli, Apr 07 2011
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EXAMPLE
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0, 1, 5/2, 9/2, 7, 10, 27/2, 35/2, 22, 27, ...
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MATHEMATICA
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f[n_] := n/GCD[n, 4]; Array[f[#] f[# + 3] &, 58]
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PROG
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(PARI) s=vector(40, n, 1/4*(n+2)*(n-1)) /* fractions */
vector(#s, n, numerator(s[n])) /* this sequence */- from J. Arndt, Jan 04 2011
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CROSSREFS
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Cf. A130658 (denominators), A033954 (quadrisection), A001107 (quadrisection), A181890 (quadrisection).
Sequence in context: A086055 A219734 A077125 * A055566 A153610 A217249
Adjacent sequences: A160047 A160048 A160049 * A160051 A160052 A160053
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KEYWORD
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nonn,easy,frac
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AUTHOR
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Eric W. Weisstein, Apr 30 2009
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EXTENSIONS
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Edited by N. J. A. Sloane, Dec 23 2010
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STATUS
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approved
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