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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,...

%I A086514 #18 Jun 13 2015 00:51:06
%S A086514 1,2,3,6,13,26,47,78,121,178,251,342,453,586,743,926,1137,1378,1651,
%T A086514 1958,2301,2682,3103,3566,4073,4626,5227,5878,6581,7338,8151,9022,
%U A086514 9953,10946,12003,13126,14317,15578,16911,18318,19801,21362,23003,24726
%N 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,...
%C A086514 {a(k): 1 <= k <= 4} = divisors of 6. - _Reinhard Zumkeller_, Jun 17 2009
%H A086514 B. Berselli, <a href="/A086514/b086514.txt">Table of n, a(n) for n = 1..10000</a> - _Bruno Berselli_, May 31 2010
%H A086514 R. Zumkeller, <a href="/A161700/a161700.txt">Enumerations of Divisors</a> - _Reinhard Zumkeller_, Jun 17 2009
%H A086514 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A086514 a(n)+ n-2 = {a(n-1) +a(n+1)}/2
%F A086514 a(n) = (n^3-6*n^2+14*n-6)/3.
%F A086514 Contribution from _Bruno Berselli_, May 31 2010: (Start)
%F A086514 G.f.: (1-2*x+x^2+2*x^3)/(1-x)^4.
%F A086514 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.
%F A086514 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)
%e A086514 2 = (1+3)/2 -0. 3 = (2+6)/2 - 1, 6 = (3+13)/2 - 2, etc.
%o A086514 (PARI) a(n) = n*(n^2-6*n+14)/3-2 \\ _Charles R Greathouse IV_, Jun 11 2015
%Y A086514 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.
%K A086514 nonn,easy
%O A086514 1,2
%A A086514 _Amarnath Murthy_, Jul 29 2003
%E A086514 More terms from _David Wasserman_, Mar 10 2005