A028401 The (2^n+1)-th triangular number (cf. A000217).

3, 6, 15, 45, 153, 561, 2145, 8385, 33153, 131841, 525825, 2100225, 8394753, 33566721, 134242305, 536920065, 2147581953, 8590131201, 34360131585, 137439739905, 549757386753, 2199026401281, 8796099313665, 35184384671745

Offset

2,1

Comments

Number of types of Boolean functions of n variables under a certain group.

Also the number of ordered decompositions of 2^n into 3 nonnegative integers (e.g., 2 = 0+0+2 = 0+2+0 = 2+0+0 = 1+1+0 = 1+0+1 = 0+1+1). - Tamas Kalmar-Nagy (integers(AT)kalmarnagy.com), Aug 02 2007

Links

Vincenzo Librandi, Table of n, a(n) for n = 2..1000

Daniel Poveda Parrilla, Illustration of initial terms

I. Strazdins, Universal affine classification of Boolean functions, Acta Applic. Math. 46 (1997), 147-167.

Index entries for sequences related to Boolean functions

Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

Formula

From Ralf Stephan, Aug 23 2003: (Start)

a(n) = (3/8)*2^n + (1/32)*4^n + 1.

a(n) = 3*A007581(n-2) = (3/4)*A060919(n-1). (End)

a(n) = (2^n+4)*(2^n+8)/32. - Tamas Kalmar-Nagy (integers(AT)kalmarnagy.com), Aug 02 2007

G.f.: 3*x^2*(1-5*x+5*x^2)/((1-x)*(1-2*x)*(1-4*x)). - Colin Barker, Mar 09 2012

a(n) = a(n-1) + 3*A000217(2^(n-3)) for n > 2. - Daniel Poveda Parrilla, Dec 27 2016

Mathematica

Drop[#, 2] &@ CoefficientList[Series[3 x^2*(1 - 5 x + 5 x^2)/((1 - x) (1 - 2 x) (1 - 4 x)), {x, 0, 25}], x] (* Michael De Vlieger, Jul 08 2019 *)

Crossrefs

Equals 2*A036562(n-4) - 1, n > 3.

Cf. A000217.

Sequence in context: A289678 A337326 A056382 * A005655 A277063 A051169

Adjacent sequences: A028398 A028399 A028400 * A028402 A028403 A028404

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vladeta Jovovic, Feb 24 2000

Simpler definition from Tamas Kalmar-Nagy (integers(AT)kalmarnagy.com), Aug 02 2007

Status

approved