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Search: id:A089708
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| A089708 |
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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. |
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+0
1
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| 1, 2, 3, 7, 26, 136, 887, 6785, 59116, 576528, 6215729, 73368729, 940718528, 13016462714, 193285275705, 3065510539375, 51713071208774, 924496937994286, 17458742846249615, 347270877144570683, 7256791451501057782
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OFFSET
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1,2
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FORMULA
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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 (dean(AT)math.ucdavis.edu), Nov 15 2003
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EXAMPLE
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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.
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MATHEMATICA
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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]
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CROSSREFS
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Sequence in context: A091230 A063852 A092983 this_sequence A107881 A128001 A052877
Adjacent sequences: A089705 A089706 A089707 this_sequence A089709 A089710 A089711
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 14 2003
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EXTENSIONS
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Edited by Dean Hickerson (dean(AT)math.ucdavis.edu) and Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 15 2003
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