A067239 a(0)=1, a(n) = 8n*(2n-1).

1, 8, 48, 120, 224, 360, 528, 728, 960, 1224, 1520, 1848, 2208, 2600, 3024, 3480, 3968, 4488, 5040, 5624, 6240, 6888, 7568, 8280, 9024, 9800, 10608, 11448, 12320, 13224, 14160, 15128, 16128, 17160, 18224, 19320, 20448, 21608, 22800, 24024

Offset

0,2

Comments

Engel expansion of cosh(1/2).

Also, 8 times hexagonal numbers (A000384(n)*8 = A152750(n)), for n>0. - Omar E. Pol, Dec 14 2008

Links

Table of n, a(n) for n=0..39.

Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).

Formula

a(n) = a(n-1) + 32*n - 24 (with a(1)=8). - Vincenzo Librandi, Dec 15 2010

From Colin Barker, Apr 13 2012: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.

G.f.: (1 + 5*x + 27*x^2 - x^3)/(1-x)^3. (End)

Mathematica

s=0; lst={s}; Do[s+=n++ +8; AppendTo[lst, s], {n, 0, 8!, 32}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 16 2008 *)

Prog

(PARI) Vec((1+5*x+27*x^2-x^3)/(1-x)^3+O(x^99)) \\ Charles R Greathouse IV, Apr 13 2012

Crossrefs

Cf. A006784 for Engel expansion definition.

Sequence in context: A121028 A139279 A250257 * A152750 A121355 A227499

Adjacent sequences: A067236 A067237 A067238 * A067240 A067241 A067242

Keyword

easy,nonn

Author

Benoit Cloitre, Mar 03 2002

Status

approved