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A081441
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a(n) = (2*n^3 - n^2 - n + 2)/2.
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3
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1, 1, 6, 22, 55, 111, 196, 316, 477, 685, 946, 1266, 1651, 2107, 2640, 3256, 3961, 4761, 5662, 6670, 7791, 9031, 10396, 11892, 13525, 15301, 17226, 19306, 21547, 23955, 26536, 29296, 32241, 35377, 38710, 42246, 45991, 49951, 54132, 58540, 63181
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OFFSET
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0,3
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COMMENTS
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Diagonal in array of n-gonal numbers A081422.
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LINKS
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FORMULA
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G.f.: (1 -4*x +11*x^2 -8*x^3)/(1-x)^5.
E.g.f.: (2 + 5*x^2 + 2*x^3)*exp(x)/2. - G. C. Greubel, Aug 14 2019
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MAPLE
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a:= n-> (2*n^3-n^2-n+2)/2: seq(a(n), n=0..50); # Zerinvary Lajos, Sep 13 2006
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MATHEMATICA
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CoefficientList[Series[(1 - 4 x + 11 x^2 - 8 x^3) / (1 - x)^5, {x, 0, 50}], x] (* Vincenzo Librandi, Aug 08 2013 *)
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PROG
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(PARI) vector(40, n, n--; (2*n^3-n^2-n+2)/2) \\ G. C. Greubel, Aug 14 2019
(Sage) [(2*n^3-n^2-n+2)/2 for n in (0..40)] # G. C. Greubel, Aug 14 2019
(GAP) List([0..40]. n-> (2*n^3-n^2-n+2)/2); # G. C. Greubel, Aug 14 2019
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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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