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A276805
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a(n) = numerator((n^2 + 3*n + 2)/n^3).
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2
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6, 3, 20, 15, 42, 7, 72, 45, 110, 33, 156, 91, 210, 30, 272, 153, 342, 95, 420, 231, 506, 69, 600, 325, 702, 189, 812, 435, 930, 124, 1056, 561, 1190, 315, 1332, 703, 1482, 195, 1640, 861, 1806, 473, 1980, 1035, 2162, 282, 2352, 1225, 2550, 663, 2756, 1431, 2970, 385
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OFFSET
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1,1
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,-3,0,0,0,0,0,0,0,1).
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FORMULA
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a(n) = 3*a(n-8)-3*a(n-16)+a(n-24) for n>24.
G.f.: x*(6 +3*x +20*x^2 +15*x^3 +42*x^4 +7*x^5 +72*x^6 +45*x^7 +92*x^8 +24*x^9 +96*x^10 +46*x^11 +84*x^12 +9*x^13 +56*x^14 +18*x^15 +30*x^16 +5*x^17 +12*x^18 +3*x^19 +2*x^20 +x^23) / ((1 -x)^3*(1 +x)^3*(1 +x^2)^3*(1 +x^4)^3).
(End)
a(n) = a(n-8)*(n^2+3*n+2)/(n^2-13*n+42), for n>8. - Gionata Neri, Feb 25 2017
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EXAMPLE
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a(1) = numerator((n^2 + 3*n + 2)/n^3) = 1^2+3*1+2/1^3 = 6.
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MATHEMATICA
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Table[Numerator[(n^2 + 3*n + 2)/n^3], {n, 1, 100}]
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PROG
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(PARI) a(n) = numerator((n^2 + 3*n + 2)/n^3); \\ Michel Marcus, Sep 18 2016
(PARI) Vec(x*(6 +3*x +20*x^2 +15*x^3 +42*x^4 +7*x^5 +72*x^6 +45*x^7 +92*x^8 +24*x^9 +96*x^10 +46*x^11 +84*x^12 +9*x^13 +56*x^14 +18*x^15 +30*x^16 +5*x^17 +12*x^18 +3*x^19 +2*x^20 +x^23) / ((1 -x)^3*(1 +x)^3*(1 +x^2)^3*(1 +x^4)^3) + O(x^100)) \\ Colin Barker, Oct 20 2016
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CROSSREFS
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KEYWORD
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nonn,easy,frac
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AUTHOR
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STATUS
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approved
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