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A059997
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a(n) = (n/2)*(n + 1)*(3*n + 11).
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2
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14, 51, 120, 230, 390, 609, 896, 1260, 1710, 2255, 2904, 3666, 4550, 5565, 6720, 8024, 9486, 11115, 12920, 14910, 17094, 19481, 22080, 24900, 27950, 31239, 34776, 38570, 42630, 46965, 51584, 56496, 61710, 67235, 73080, 79254, 85766, 92625
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OFFSET
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1,1
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COMMENTS
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Number of dimensions for non-compact n-manifolds.
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REFERENCES
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Harold W. Kuhn and Sylvia Nasar, eds., The Essential John Nash, Princeton University Press, Princeton, NJ, 2002, Chapter 11, page 207.
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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).
G.f.: x*(14-5*x)/(1-x)^4. (End)
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MATHEMATICA
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Table[3/2n^3 + 7n^2 + 11/2n, {n, 1, 40}]
LinearRecurrence[{4, -6, 4, -1}, {14, 51, 120, 230}, 40] (* Harvey P. Dale, Apr 06 2022 *)
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PROG
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(PARI) { for (n=1, 1000, write("b059997.txt", n, " ", n*(n + 1)*(3*n + 11)/2); ) } \\ Harry J. Smith, Jul 01 2009
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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