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 A086514 Difference between the arithmetic mean of the neighbors of the terms and the term itself follows the pattern 0,1,2,3,4,5,... 22
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS {a(k): 1 <= k <= 4} = divisors of 6. - Reinhard Zumkeller, Jun 17 2009 LINKS B. Berselli, Table of n, a(n) for n = 1..10000 - Bruno Berselli, May 31 2010 R. Zumkeller, Enumerations of Divisors - Reinhard Zumkeller, Jun 17 2009 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA 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) EXAMPLE 2 = (1+3)/2 -0. 3 = (2+6)/2 - 1, 6 = (3+13)/2 - 2, etc. PROG (PARI) a(n) = n*(n^2-6*n+14)/3-2 \\ Charles R Greathouse IV, Jun 11 2015 CROSSREFS Cf. A005408, A000124, A016813, A000125, A058331, A002522, A161701, A161702, A161703, A000127, A161704, A161706, A161707, A161708, A161710, A080856, A161711, A161712, A161713, A161715, A006261, A177342, A014106, A000290. Sequence in context: A240104 A018274 A018775 * A079662 A290991 A007910 Adjacent sequences:  A086511 A086512 A086513 * A086515 A086516 A086517 KEYWORD nonn,easy AUTHOR Amarnath Murthy, Jul 29 2003 EXTENSIONS More terms from David Wasserman, Mar 10 2005 STATUS approved

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Last modified October 14 02:29 EDT 2019. Contains 327995 sequences. (Running on oeis4.)