login
A092236
a(n) = (3^n + 2*3^(n/2)*cos(n*Pi/6))/3.
0
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.
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 18 2004
STATUS
approved