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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. [From Reinhard Zumkeller, Jun 17 2009]

LINKS

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).

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.

CROSSREFS

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: A240104 A018274 A018775 * A079662 A007910 A052702

Adjacent sequences:  A086511 A086512 A086513 * A086515 A086516 A086517

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Jul 29 2003

EXTENSIONS

More terms from David Wasserman, Mar 10 2005

STATUS

approved

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Last modified September 23 16:20 EDT 2014. Contains 247172 sequences.