A059997 a(n) = (n/2)*(n + 1)*(3*n + 11).

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

Offset

1,1

Comments

Number of dimensions for non-compact n-manifolds.

References

Harold W. Kuhn and Sylvia Nasar, eds., The Essential John Nash, Princeton University Press, Princeton, NJ, 2002, Chapter 11, page 207.

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

John Nash, The Imbedding Problem For Riemannian Manifolds, Annals of Mathematics, Vol. 63, No. 1, 1956, pp. 20-63.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

From Colin Barker, Jan 28 2012: (Start)

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)

Mathematica

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 *)

Prog

(PARI) a(n) = { n*(n + 1)*(3*n + 11)/2 } \\ Harry J. Smith, Jul 01 2009

Crossrefs

Sequence in context: A043912 A244804 A009961 * A007588 A269312 A129025

Adjacent sequences: A059994 A059995 A059996 * A059998 A059999 A060000

Keyword

easy,nonn,changed

Author

Jason Earls, Mar 10 2001

Extensions

Edited by Robert G. Wilson v, Mar 02 2002

Status

approved