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A027658
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a(n) = binomial(n+2, 2) + binomial(n+4, 5).
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3
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1, 4, 12, 31, 71, 147, 280, 498, 837, 1342, 2068, 3081, 4459, 6293, 8688, 11764, 15657, 20520, 26524, 33859, 42735, 53383, 66056, 81030, 98605, 119106, 142884, 170317, 201811, 237801, 278752, 325160, 377553, 436492, 502572, 576423, 658711, 750139, 851448
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (1 - 2*x + 3*x^2 - x^3)/(1-x)^6. - Colin Barker, Apr 15 2013
a(n) = (n+1)*(n+2)*(60 +12*n +7*n^2 +n^3)/120. (End)
a(n) = Sum_{j=1..2} binomial(n+2*j, 3*j-1).
E.g.f.: (1/120)*(120 + 360*x + 300*x^2 + 120*x^3 + 20*x^4 + x^5)*exp(x). (End)
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MATHEMATICA
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CoefficientList[Series[(1-2*x+3*x^2-x^3)/(1-x)^6, {x, 0, 60}], x] (* Vincenzo Librandi, Oct 18 2013 *)
Sum[Binomial[2*j +Range[0, 60], 3*j-1], {j, 2}] (* G. C. Greubel, Aug 01 2022 *)
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 4, 12, 31, 71, 147}, 40] (* Harvey P. Dale, Feb 27 2023 *)
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PROG
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(Magma) [(60 +12*n +7*n^2 +n^3)*Binomial(n+2, 2)/60: n in [0..60]]; // G. C. Greubel, Aug 01 2022
(SageMath) [(60 +12*n +7*n^2 +n^3)*binomial(n+2, 2)/60 for n in (0..60)] # G. C. Greubel, Aug 01 2022
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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