A155609 a(n) = 4^n - 3^n + 1.

1, 2, 8, 38, 176, 782, 3368, 14198, 58976, 242462, 989528, 4017158, 16245776, 65514542, 263652488, 1059392918, 4251920576, 17050729022, 68332056248, 273715645478, 1096024843376, 4387586157902, 17560804984808, 70274600998838

Offset

0,2

Comments

Let P(A) be the power set of an n-element set A and R be a relation on P(A) such that for all x, y of P(A), xRy if x and y are intersecting. Then a(n) = |R|. - Ross La Haye, Mar 19 2009

Links

Table of n, a(n) for n=0..23.

Ross La Haye, Binary Relations on the Power Set of an n-Element Set, Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6.

Index entries for linear recurrences with constant coefficients, signature (8,-19,12).

Formula

G.f.: 1/(1-4*x) - 1/(1-3*x) + 1/(1-x).

E.g.f.: exp(4*x) - exp(3*x) + exp(x).

a(n) = 7*a(n-1)-12*a(n-2)+6 with a(0)=1, a(1)=2. - Vincenzo Librandi, Jul 21 2010

Mathematica

Table[4^n-3^n+1, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011 *)
LinearRecurrence[{8, -19, 12}, {1, 2, 8}, 30] (* Harvey P. Dale, Sep 30 2018 *)

Prog

(PARI) a(n)=4^n-3^n+1 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A155596, A155597, A155598, A155599, A155600, A155601, A155602, A155603, A155604, A155605, A155606, A155607, A155608.

Sequence in context: A112738 A220806 A192529 * A220542 A199213 A002003

Adjacent sequences: A155606 A155607 A155608 * A155610 A155611 A155612

Keyword

nonn,easy

Author

Mohammad K. Azarian, Jan 26 2009

Status

approved