A092236 a(n) = (3^n + 2*3^(n/2)*cos(n*Pi/6))/3.

1, 2, 4, 9, 24, 72, 225, 702, 2160, 6561, 19764, 59292, 177633, 532170, 1595052, 4782969, 14346720, 43040160, 129127041, 387400806, 1162241784, 3486784401, 10460412252, 31381236756, 94143533121, 282430067922, 847289140884, 2541865828329, 7625595890664

Offset

0,2

Comments

From an Internat. Math. Olympiad problem.

Comment from Neil Fernandez, Apr 29 2014: The question was proposed at the IMO in 1992 and got on to the long list, as question 19, but not the shortlist.

References

E. Lozansky and C. Rousseau, Winning Solutions, Springer, 1996; see p. 154.

Links

Table of n, a(n) for n=0..28.

The Art of Problem Solving, IMO Longlists 1992 (From Neil Fernandez, Jul 29 2014)

Index entries for linear recurrences with constant coefficients, signature (6,-12,9).

Formula

G.f.: (1 - 4*x + 4*x^2)/((1 - 3*x)*(1 - 3*x + 3*x^2)).

a(n) = Sum_{k=0..n} binomial(n, k) * Sum_{j=0..floor(k/3)} binomial(k, 3*j). - Joseph M. Shunia, Jul 25 2022

Crossrefs

Sequence in context: A148084 A156804 A081913 * A367112 A336023 A009283

Adjacent sequences: A092233 A092234 A092235 * A092237 A092238 A092239

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 18 2004

Status

approved