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A191993 a(n) = 3^(n-1) + C(2*n, n)/2. 1
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 (list; graph; refs; listen; history; text; internal format)
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. 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

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Last modified October 20 16:07 EDT 2021. Contains 348111 sequences. (Running on oeis4.)