A026740 a(n) = 2^n*(2^n - 1)*(2^n - 2)/6.

0, 0, 4, 56, 560, 4960, 41664, 341376, 2763520, 22238720, 178433024, 1429559296, 11444858880, 91592417280, 732873539584, 5863525154816, 46910348656640, 375291379056640, 3002365391929344, 24019060573863936, 192153034345676800, 1537226473786572800

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Jan Brandts and Apo Cihangir, Counting triangles that share their vertices with the unit n-cube, in Conference Applications of Mathematics 2013 in honor of the 70th birthday of Karel Segeth. Jan Brandts, Sergey Korotov, et al., eds., Institute of Mathematics AS CR, Prague 2013.

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

Formula

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

a(n) = 14*a(n-1) - 56*a(n-2) + 64*a(n-3) for n>=3. - Harvey P. Dale, Jun 20 2012

From Elmo R. Oliveira, Mar 20 2026: (Start)

G.f.: -4*x^2/((8*x - 1)*(4*x - 1)*(2*x - 1)).

E.g.f.: exp(2*x)*(2 - 3*exp(2*x) + exp(6*x))/6.

a(n) = 4*A016290(n-2) for n >= 2. (End)

Maple

seq(binomial(2^n, 3), n=0..20); # Zerinvary Lajos, Feb 22 2008

Mathematica

Binomial[2^Range[0, 20], 3] (* or *) LinearRecurrence[{14, -56, 64}, {0, 0, 4}, 21] (* Harvey P. Dale, Jun 20 2012 *)

Prog

(Magma) [2^n*(2^n-1)*(2^n-2)/6: n in [0..20]]; // Vincenzo Librandi, May 23 2011
(PARI) vector(20, n, binomial(2^(n-1), 6)) \\ G. C. Greubel, Oct 26 2019
(SageMath) [binomial(2^n, 6) for n in (0..20)] # G. C. Greubel, Oct 26 2019
(GAP) List([0..20], n-> Binomial(2^n, 3)); # G. C. Greubel, Oct 26 2019

Crossrefs

Cf. A000079, A006516, A016290.

Sequence in context: A101540 A358882 A224181 * A191466 A333294 A130219

Adjacent sequences: A026737 A026738 A026739 * A026741 A026742 A026743

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved