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A027625
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Numerator of n*(n+5)/((n+2)*(n+3)).
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2
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0, 1, 7, 4, 6, 25, 11, 14, 52, 21, 25, 88, 34, 39, 133, 50, 56, 187, 69, 76, 250, 91, 99, 322, 116, 125, 403, 144, 154, 493, 175, 186, 592, 209, 221, 700, 246, 259, 817, 286, 300, 943, 329, 344, 1078, 375, 391, 1222
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: x*(1 + 7*x + 4*x^2 + 3*x^3 + 4*x^4 - x^5 - x^6 - 2*x^7)/(1 - x^3)^3.
a(n) = numerator of n*(n+5)/6. - Altug Alkan, Apr 18 2018
a(n) is quasi-polynomial in n:
a(3*n) = (1/2)*n*(3*n+5) = A115067(n+1).
a(3*n+1) = (1/2)*(n+2)*(3*n+1) = A095794(n+1).
a(3*n+2) = (1/2)*(3*n+2)*(3*n+7) = A179436(n). (End)
Sum_{n>=1} 1/a(n) = 4*Pi/(15*sqrt(3)) + 87/50. - Amiram Eldar, Aug 11 2022
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MATHEMATICA
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CoefficientList[Series[x*(1+7*x+4*x^2+3*x^3+4*x^4-x^5-x^6-2*x^7)/(1-x^3)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Mar 04 2014 *)
Numerator[25*Binomial[Range[0, 50]/5 +1, 2]/3] (* G. C. Greubel, Aug 05 2022 *)
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PROG
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(Magma) [Numerator(n*(n+5)/((n+2)*(n+3))): n in [0..50]]; // Vincenzo Librandi, Mar 04 2014
(PARI) a(n) = numerator(n*(n+5)/6); \\ Altug Alkan, Apr 18 2018
(SageMath) [numerator(n*(n+5)/6) for n in (0..50)] # G. C. Greubel, Aug 05 2022
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CROSSREFS
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KEYWORD
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nonn,frac,easy
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AUTHOR
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STATUS
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approved
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