A093356 Number of occurrences of pattern 1-2 after n iterations of morphism A007413.

3, 8, 28, 104, 400, 1568, 6208, 24704, 98560, 393728, 1573888, 6293504, 25169920, 100671488, 402669568, 1610645504, 6442516480, 25769934848, 103079477248, 412317384704, 1649268490240, 6597071863808, 26388283260928

Offset: 1

Author

Ralf Stephan, Apr 27 2004

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• S. Kitaev and T. Mansour, Counting the occurrences of generalized patterns....
• Index entries for linear recurrences with constant coefficients, signature (6, -8).

Programs

Magma

[Ceiling((3*(4^(n-1)) + 2^n)/2): n in [1..30]]; // Vincenzo Librandi, Oct 03 2011

Mathematica

Join[{3},Table[(3*4^(n-1)+2^n)/2,{n,2,30}]] (* or *) Join[{3}, LinearRecurrence[ {6,-8},{8,28},30]] (* Harvey P. Dale, Oct 02 2011 *)

PARI

a(n)=(3*4^(n-1)+2^n)/2

Formula

a(n) = (3*4^(n-1) + 2^n)/2, a(1) = 3.

G.f.: (6 - 20*x + 8*x^2)/((1-2*x)*(1-4*x)).

a(n) = 6*a(n-1) - 8*a(n-2); a(1)=3, a(2)=8, a(3)=28. -Harvey P. Dale, Oct 02 2011