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A093356 Number of occurrences of pattern 1-2 after n iterations of morphism A007413. 1
3, 8, 28, 104, 400, 1568, 6208, 24704, 98560, 393728, 1573888, 6293504, 25169920, 100671488, 402669568, 1610645504, 6442516480, 25769934848, 103079477248, 412317384704, 1649268490240, 6597071863808, 26388283260928 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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).

FORMULA

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

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

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

PROG

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

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

CROSSREFS

Sequence in context: A151431 A245892 A263103 * A224271 A135583 A009437

Adjacent sequences:  A093353 A093354 A093355 * A093357 A093358 A093359

KEYWORD

nonn

AUTHOR

Ralf Stephan, Apr 27 2004

STATUS

approved

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Last modified November 23 09:38 EST 2017. Contains 295115 sequences.