A191993 a(n) = 3^(n-1) + C(2*n, n)/2.

2, 6, 19, 62, 207, 705, 2445, 8622, 30871, 112061, 411765, 1529225, 5731741, 21652623, 82341729, 314889102, 1209849831, 4666707813, 18060052389, 70085525877, 272615721621, 1062509835063, 4148096423409, 16217945020377, 63487732755357, 248806555083495

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Mircea Merca, A Note on Cosine Power Sums J. Integer Sequences, Vol. 15 (2012), Article 12.5.3.

Formula

a(n) = A000244(n-1) + A001700(n-1).

a(n) = Sum_{k=0..floor(n/3)} (-1)^k*C(2*n, n-3*k).

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

Conjecture: n*(n-3)*a(n) - (7*n^2 -23*n +12)*a(n-1) +6*(2*n-3)*(n-2)*a(n-2)=0. - R. J. Mathar, Oct 18 2017

Example

a(5) = 3^4 + C(10,5)/2 = 81 + 126 = 207.

Maple

seq(3^(n-1)+binomial(2*n-1, n), n=1..20)

Mathematica

Table[3^(n-1)+Binomial[2n, n]/2, {n, 30}] (* Harvey P. Dale, Dec 27 2011 *)

Prog

(PARI) a(n)=3^(n-1)+binomial(n+n, n)/2 \\ Charles R Greathouse IV, Jun 21 2011

Crossrefs

Cf. A000244, A001700, A005317.

Sequence in context: A033193 A071738 A026012 * A120900 A284216 A059712

Adjacent sequences: A191990 A191991 A191992 * A191994 A191995 A191996

Keyword

nonn,easy

Author

Mircea Merca, Jun 21 2011

Status

approved