OFFSET
1,2
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
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Nov 14 2003
EXTENSIONS
Edited by Dean Hickerson and Ray Chandler, Nov 15 2003
STATUS
approved