A092055 a(n) = binomial(2+2^n,3).

1, 4, 20, 120, 816, 5984, 45760, 357760, 2829056, 22500864, 179481600, 1433753600, 11461636096, 91659526144, 733141975040, 5864598896640, 46914643623936, 375308558925824, 3002434111406080, 24019335451770880, 192154133857304576, 1537230871833083904, 12297838178567454720

Offset

0,2

Comments

a(n) = Sum_{i=1...(2^n)} i*(i+1)/2, this sequence is thus similar to A016131 as it is a sum of triangular numbers on the interval <1,2^n>, A016131 is a sum of triangular numbers on the interval <1,2^n - 1>. - Ctibor O. Zizka, Mar 03 2009

a(n) is the number of unordered (not necessarily distinct) triples of subsets taken from the power set of {1,2,...,n}. Cf. A007582 (pairs of such subsets). - Geoffrey Critzer, Jul 10 2013

Links

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (14,-56,64).

Formula

a(n) = (2^(3n-1) +3*2^(2n-1) + 2^n)/3 = A092056(3, n) = A007581(n)*A000079(n) = 2*a(n-1)+4^(n-1)+8^(n-1).

a(n) = [x^3] 1/(1-x)^(2^n). - Geoffrey Critzer, Jul 11 2013

a(n) = 14*a(n-1)-56*a(n-2)+64*a(n-3). - Colin Barker, Sep 13 2014

G.f.: -(20*x^2-10*x+1) / ((2*x-1)*(4*x-1)*(8*x-1)). - Colin Barker, Sep 13 2014

Example

a(5) = C(2+2^5,3) = C(34,3) = 5984.

Maple

seq(binomial(2+2^n, 3), n=0..25); # Zerinvary Lajos, Feb 22 2008

Mathematica

nn=20; Table[Coefficient[Series[1/(1-x)^(2^n), {x, 0, nn}], x^3], {n, 0, nn}] (* Geoffrey Critzer, Jul 10 2013 *)

Prog

(PARI) Vec(-(20*x^2-10*x+1)/((2*x-1)*(4*x-1)*(8*x-1)) + O(x^100)) \\ Colin Barker, Sep 13 2014

Crossrefs

Cf. A016131. - Ctibor O. Zizka, Mar 03 2009

Sequence in context: A046729 A277920 A093123 * A187848 A370653 A001715

Adjacent sequences: A092052 A092053 A092054 * A092056 A092057 A092058

Keyword

nonn,easy

Author

Henry Bottomley, Feb 19 2004

Status

approved