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,...

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

Offset: 1

Author

Amarnath Murthy, Jul 29 2003

Keywords

• nonn
• easy

Comments

{a(k): 1 <= k <= 4} = divisors of 6. - Reinhard Zumkeller, Jun 17 2009

Examples

			2 = (1+3)/2 -0. 3 = (2+6)/2 - 1, 6 = (3+13)/2 - 2, etc.
		

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).

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.

Programs

PARI

a(n) = n*(n^2-6*n+14)/3-2 \\ Charles R Greathouse IV, Jun 11 2015

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)

Extensions

More terms from David Wasserman, Mar 10 2005