A089708 a(1) = 1, a(2) = 2, a(n) = a(n-1) + d where d is the sum of the absolute differences between all pairs of previous terms.

1, 2, 3, 7, 26, 136, 887, 6785, 59116, 576528, 6215729, 73368729, 940718528, 13016462714, 193285275705, 3065510539375, 51713071208774, 924496937994286, 17458742846249615, 347270877144570683, 7256791451501057782

Offset

1,2

Links

Table of n, a(n) for n=1..21.

Formula

a(n) = a(n-1) + sum_{1<=i<j<n} (a(j)-a(i))

a(n) = (n+1)(a(n-1)-a(n-2)) + a(n-3) for n>=5.

Conjecture: a(n) = c n! (1+2/n+(5/2)/n^2+(31/6)/n^3+(317/24)/n^4+O(1/n^5)), where c is about 0.1289432494744. - Dean Hickerson, Nov 15 2003

In closed form, c = BesselJ[3,2] = 0.128943249474402051... - Vaclav Kotesovec, Nov 19 2012

Example

26 follows 7 as the sum of the differences of previous terms is (2-1) + (3-1) + (7-1) + (3-2) + (7-2) + (7-3) = 19 and 7+19 = 26.

Mathematica

a[1]=1; a[2]=2; a[3]=3; a[4]=7; a[n_] := a[n]=(n+1)(a[n-1]-a[n-2])+a[n-3]

Crossrefs

Sequence in context: A342155 A308114 A092983 * A107881 A371161 A128001

Adjacent sequences: A089705 A089706 A089707 * A089709 A089710 A089711

Keyword

nonn

Author

Amarnath Murthy, Nov 14 2003

Extensions

Edited by Dean Hickerson and Ray Chandler, Nov 15 2003

Status

approved