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Search: id:A070893
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| A070893 |
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Let r, s, t be three permutations of the set {1,2,3,...,n}; a(n)= value of Sum_{i=1..n} r(i) s(i) t(i), with r={1,2,3,..,n}; s={n,n-1,...,1} and t={n,n-2,n-4,...,1,...,n-3,n-1}. |
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+0
4
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| 1, 6, 19, 46, 94, 172, 290, 460, 695, 1010, 1421, 1946, 2604, 3416, 4404, 5592, 7005, 8670, 10615, 12870, 15466, 18436, 21814, 25636, 29939, 34762, 40145, 46130, 52760, 60080, 68136, 76976, 86649, 97206, 108699, 121182, 134710, 149340
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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See A070735 for the minimal values for these products. This series is an upper bound. The third permutation 't'= Ceiling[Abs[Range[n-1/2,-n,-2]]] is such that it associates its smallest factor with the largest factor of the product 'r'*'s'.
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LINKS
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Index entries for two-way infinite sequences
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FORMULA
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G.f.: x(1+2x)/((1+x)(1-x)^5). - Michael Somos, Apr 07 2003
a(n)=3a(n-1)-2a(n-2)-2a(n-3)+3a(n-4)-a(n-5)+3. If sequence is also defined for n <= 0 by this equation, then a(n)=0 for -3 <= n <= 0 and a(n)=A082289(-n) for n <= -4. - Michael Somos, Apr 07 2003
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EXAMPLE
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{1,2,3,4,5,6,7}*{7,6,5,4,3,2,1}*{7,5,3,1,2,4,6} gives {49,60,45,16,30,48,42}, with sum 290, so a(7)=290
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MAPLE
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with (combinat):a[0]:=0:for n from 1 to 50 do a[n]:=stirling2(n+2, n)-a[n-1] od: seq(a[n], n=1..38); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 17 2008
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MATHEMATICA
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Table[Plus@@(Range[n]*Range[n, 1, -1]*Ceiling[Abs[Range[n-1/2, -n, -2]]]), {n, 49}]; or CoefficientList[Series[ -(1+2x)/(-1+x)^5/(1+x), {x, 0, 48}], x]//Flatten
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PROGRAM
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(PARI) a(n)=sum(i=1, n, i*(n+1-i)*ceil(abs(n+3/2-2*i)))
(PARI) a(n)=polcoeff(if(n<0, x^4*(2+x)/((1+x)*(1-x)^5), x*(1+2*x)/((1+x)*(1-x)^5))+x*O(x^abs(n)), abs(n))
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CROSSREFS
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Cf. A070735, A082289. a(n)=A082290(2n-2).
Sequence in context: A005900 A138357 A005712 this_sequence A027963 A034199 A073362
Adjacent sequences: A070890 A070891 A070892 this_sequence A070894 A070895 A070896
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KEYWORD
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easy,nonn
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be), May 22 2002
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