A123198 a(n)=[(n+1)(2n-1)]^2.

1, 4, 81, 400, 1225, 2916, 5929, 10816, 18225, 28900, 43681, 63504, 89401, 122500, 164025, 215296, 277729, 352836, 442225, 547600, 670761, 813604, 978121, 1166400, 1380625, 1623076, 1896129, 2202256, 2544025, 2924100, 3345241, 3810304

Offset

0,2

References

Fredrick T. Wall, Chemical Thermodynamics, W. H, Freeman, San Francisco, 1965, page 269

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Formula

a(n)=Sum((4k-1)(4k^2-2k-1),k=0..n) (n>=0).

G.f.: (1-x+71*x^2+25*x^3)/(1-x)^5. [Colin Barker, Jan 28 2012]

Maple

a:=n->(n+1)^2*(2*n-1)^2: seq(a(n), n=0..31);

Mathematica

f[m_] = Sum[(4*n - 1)*(4*n^2 - 2*n - 1), {n, 0, m}]; a = Table[f[n], {n, 0, 50}]

Crossrefs

Sequence in context: A053901 A017006 A041189 * A202831 A335691 A264197

Adjacent sequences: A123195 A123196 A123197 * A123199 A123200 A123201

Keyword

nonn

Author

Roger L. Bagula, Oct 04 2006

Extensions

Edited by N. J. A. Sloane, Oct 15 2006

Status

approved