OFFSET
0,2
LINKS
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. [Ross La Haye, Feb 22 2009]
Index entries for linear recurrences with constant coefficients, signature (10,-35,50,-24).
FORMULA
a(n) = (1/2)(4^n - 3^(n+1) + 7*2^n - 3) = 3*StirlingS2(n+1,4) + 2*StirlingS2(n+1,2) + 1.
G.f.: (1-7*x+12*x^2+3*x^3)/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)). [Colin Barker, Jul 29 2012]
EXAMPLE
a(2) = 7 because for P(A) = {{},{1},{2},{1,2}} we have for case 0 {{},{1}}, {{},{2}}, {{},{1,2}} and we have for case 2 {{},{}}, {{1},{1}}, {{2},{2}}, {{1,2},{1,2}}. There are 0 {x,y} of P(A) in this example that fall under case 1.
MATHEMATICA
Table[3 StirlingS2[n + 1, 4] + 2 StirlingS2[n + 1, 2] + 1, {n, 0, 27}] (* Michael De Vlieger, Nov 30 2015 *)
PROG
(PARI) a(n) = (4^n - 3^(n+1) + 7*2^n - 3)/2; \\ Michel Marcus, Nov 30 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ross La Haye, Jan 11 2008
EXTENSIONS
More terms from Michael De Vlieger, Nov 30 2015
STATUS
approved