OFFSET
1,1
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
I. Strazdins, Universal affine classification of Boolean functions, Acta Applic. Math. 46 (1997), 147-167.
Index entries for linear recurrences with constant coefficients, signature (6,-8).
FORMULA
a(n) = (2^(n-1) + 1)*2^n = 2*A007582(n-1). - Ralf Stephan, Mar 24 2004
a(n) = A000079(n) * (A000079(n-1) + 1) = (A000051(n) - 1) * A000051(n-1) = A000079(n) * A000051(n-1) = (A000051(n) - 1) * (A000079(n-1) + 1) = 2^n * (2^(n-1) + 1). a(n+1) = A000079(n+1) * (A000079(n) + 1) = (A000051(n+1) - 1) * A000051(n) = A000079(n+1) * A000051(n) = (A000051(n+1) - 1) * (A000079(n) + 1) = 2^(n+1) * (2^n + 1). a(n) = A081294(n) + A000079(n) = A004171(n-1) + A000079(n) = 2^(2n-1) + 2^n. - Jaroslav Krizek, Jul 27 2009
From Colin Barker, Sep 30 2014: (Start)
a(n) = 6*a(n-1) - 8*a(n-2).
G.f.: 4*x*(1 - 3*x)/((1-2*x)*(1-4*x)). (End)
E.g.f.: (1/2)*(exp(2*x) -1)*(exp(2*x) + 3). - G. C. Greubel, Jul 07 2021
MATHEMATICA
Join[{4}, Table[FromDigits[Join[{1}, PadRight[{}, n-2, 0], {1}, PadRight[ {}, n, 0]], 2], {n, 2, 30}]] (* Harvey P. Dale, Jan 24 2021 *)
PROG
(PARI) Vec(4*x*(1-3*x)/((1-2*x)*(1-4*x)) + O(x^100)) \\ Colin Barker, Sep 30 2014
(Magma) [2^(2*n-1) +2^n: n in [1..30]]; // G. C. Greubel, Jul 07 2021
(Sage) [2^(2*n-1) +2^n for n in (1..30)] # G. C. Greubel, Jul 07 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Feb 24 2000
More terms from Colin Barker, Sep 30 2014
STATUS
approved