A093357 Number of occurrences of pattern 2-1 after n iterations of morphism A007413.

0, 4, 20, 88, 368, 1504, 6080, 24448, 98048, 392704, 1571840, 6289408, 25161728, 100655104, 402636800, 1610579968, 6442385408, 25769672704, 103078952960, 412316336128, 1649266393088, 6597067669504, 26388274872320

Offset

1,2

Links

Table of n, a(n) for n=1..23.

S. Kitaev and T. Mansour, Counting the occurrences of generalized patterns....

Index entries for linear recurrences with constant coefficients, signature (6, -8).

Formula

a(1) = 0, a(n) = {3*4^(n-1) - 2^n}/2.

G.f.: [4x-4x^2]/[(1-2x)(1-4x)].

a(1)=0, a(2)=4, a(3)=20, a(n)=6*a(n-1)-8*a(n-2) [From Harvey P. Dale, Apr 04 2012]

a(n) = 4*A010036(n-2). - R. J. Mathar, Apr 07 2022

Mathematica

Join[{0}, Table[(3*4^(n-1)-2^n)/2, {n, 2, 30}]] (* or *) Join[{0}, LinearRecurrence[{6, -8}, {4, 20}, 30]] (* Harvey P. Dale, Apr 04 2012 *)

Prog

(PARI) a(n)=if(n==1, 0, (3*4^(n-1)-2^n)/2)

Crossrefs

Sequence in context: A320936 A320937 A196953 * A027156 A017964 A017965

Adjacent sequences: A093354 A093355 A093356 * A093358 A093359 A093360

Keyword

nonn,easy

Author

Ralf Stephan, Apr 27 2004

Status

approved