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A086514
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Difference between the arithmetic mean of the neighbors of the terms and the term itself follows the pattern 0,1,2,3,4,5,...
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22
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1, 2, 3, 6, 13, 26, 47, 78, 121, 178, 251, 342, 453, 586, 743, 926, 1137, 1378, 1651, 1958, 2301, 2682, 3103, 3566, 4073, 4626, 5227, 5878, 6581, 7338, 8151, 9022, 9953, 10946, 12003, 13126, 14317, 15578, 16911, 18318, 19801, 21362, 23003, 24726
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OFFSET
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1,2
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COMMENTS
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{a(k): 1 <= k <= 4} = divisors of 6. [From Reinhard Zumkeller, Jun 17 2009]
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LINKS
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B. Berselli, Table of n, a(n) for n = 1..10000 [From Bruno Berselli, May 31 2010]
R. Zumkeller, Enumerations of Divisors [From Reinhard Zumkeller, Jun 17 2009]
Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
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a(n)+ n-2 = {a(n-1) +a(n+1)}/2
a(n) = (n^3-6*n^2+14*n-6)/3.
Contribution from Bruno Berselli, May 31 2010: (Start)
G.f.: (1-2*x+x^2+2*x^3)/(1-x)^4.
a(n)-4*a(n-1)+6*a(n-2)-4*a(n-3)+a(n-4) = 0 with n>4. For n=9, 121-4*78+6*47-4*26+13 = 0.
a(n) = ( A177342(n)-A000290(n-1)-3*A014106(n-2) )/4 with n>1. For n=11, a(11) = (1671-100-3*189)/4 = 251. (End)
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EXAMPLE
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2 = (1+3)/2 -0. 3 = (2+6)/2 - 1, 6 = (3+13)/2 - 2, etc.
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CROSSREFS
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A005408, A000124, A016813, A000125, A058331, A002522, A161701, A161702, A161703, A000127, A161704, A161706, A161707, A161708, A161710, A080856, A161711, A161712, A161713, A161715, A006261. [From Reinhard Zumkeller, Jun 17 2009]
Cf. A177342, A014106 and A000290. [From Bruno Berselli, May 31 2010]
Sequence in context: A155996 A018274 A018775 * A079662 A007910 A052702
Adjacent sequences: A086511 A086512 A086513 * A086515 A086516 A086517
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 29 2003
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EXTENSIONS
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More terms from David Wasserman, Mar 10 2005
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STATUS
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approved
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