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A003777
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a(n) = n^3 + n^2 - 1.
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6
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1, 11, 35, 79, 149, 251, 391, 575, 809, 1099, 1451, 1871, 2365, 2939, 3599, 4351, 5201, 6155, 7219, 8399, 9701, 11131, 12695, 14399, 16249, 18251, 20411, 22735, 25229, 27899, 30751, 33791, 37025, 40459, 44099, 47951, 52021, 56315, 60839, 65599, 70601, 75851
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OFFSET
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1,2
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COMMENTS
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a(n) is the area of a triangle with vertices at points (n-1,(n-1)^2), (n,n^2), and ((n+1)^2,n+1). - J. M. Bergot, Jun 03 2014
Old name was: "Number of stacks of n pikelets, distance 3 flips from a well-ordered stack".
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LINKS
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FORMULA
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a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4. - Wesley Ivan Hurt, Oct 08 2017
E.g.f.: 1 + (-1 + 2*x + 4*x^2 + x^3)*exp(x). - G. C. Greubel, Jan 03 2024
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MAPLE
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MATHEMATICA
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CoefficientList[Series[(1 + 7 x - 3 x^2 + x^3)/(1-x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 20 2013 *)
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PROG
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(SageMath) [n^3+n^2-1 for n in range(1, 51)] # G. C. Greubel, Jan 03 2024
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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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EXTENSIONS
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STATUS
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approved
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