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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
R. Zumkeller, Enumerations of Divisors - Reinhard Zumkeller, Jun 17 2009
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
Sequence in context: A240104 A018274 A018775 * A079662 A290991 A007910
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 March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)