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, 26533, 28426

Offset

1,2

Comments

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

Links

Bruno Berselli, Table of n, a(n) for n = 1..10000

Reinhard Zumkeller, Enumerations of Divisors

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.

Mathematica

A086514[n_] := n*((n - 6)*n + 14)/3 - 2; Array[A086514, 50] (* Paolo Xausa, May 06 2026 *)

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