A016283 a(n) = 6^n/8 - 4^(n-1) + 2^(n-3).

0, 0, 1, 12, 100, 720, 4816, 30912, 193600, 1194240, 7296256, 44301312, 267904000, 1615810560, 9728413696, 58504691712, 351565004800, 2111537479680, 12677814747136, 76101248090112, 456744927232000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Number of rectangles that can be formed from the vertices of an n-dimensional cube. E.g., a(3)=12 because the three-dimensional cube has six faces plus six rectangles passing through the center of the cube. Cf. A064436: each rectangle on the cube provides an opportunity for a function not to be a linear threshold function, by alternating in value around the rectangle. - Matthew Cook, Jan 26 2004

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..150
• Index entries for linear recurrences with constant coefficients, signature (12, -44, 48).

Crossrefs

Third column of triangle A075497.

Cf. A025966.

Programs

Magma

[6^n/8 - 4^(n-1) + 2^(n-3): n in [0..25]]; // Vincenzo Librandi, Apr 26 2011

Maple

[seq(9/2*6^n-4*4^n+1/2*2^n,n=0..20)]; # Detlef Pauly (dettodet(AT)yahoo.de), Dec 04 2001

Mathematica

CoefficientList[Series[x^2/((1 - 2 x) (1 - 4 x) (1 - 6 x)), {x, 0, 20}], x] (* Michael De Vlieger, Jan 31 2018 *)

Sage

[((6^n - 2^n)/4-(4^n - 2^n)/2)/2 for n in range(0,21)] # Zerinvary Lajos, Jun 05 2009

Formula

a(n) = (2^n)*Stirling2(n+3, 3), n >= 0, with Stirling2(n, m) = A008277(n, m).

G.f.: x^2/((1-2*x)*(1-4*x)*(1-6*x)).

E.g.f.: (exp(2*x) - 8*exp(4*x) + 9*exp(6*x))/2!.

a(n) =((6^n - 2^n)/4 - (4^n - 2^n)/2)/2 , n >= 0. - Zerinvary Lajos, Jun 05 2009