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A037576 Base-4 digits are, in order, the first n terms of the periodic sequence with initial period 1,3. 7
1, 7, 29, 119, 477, 1911, 7645, 30583, 122333, 489335, 1957341, 7829367, 31317469, 125269879, 501079517, 2004318071, 8017272285, 32069089143, 128276356573, 513105426295, 2052421705181, 8209686820727, 32838747282909 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Rule 190

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Index entries for linear recurrences with constant coefficients, signature (4,1,-4).

FORMULA

G.f.: x*(1+3*x)/((1-x)*(1-4*x)*(1+x)). - Vincenzo Librandi, Jun 22 2012

a(n) = 4*a(n-1) + a(n-2) - 4*a(n-3). - Vincenzo Librandi, Jun 22 2012

a(n) = (28*4^n - 3*(-1)^n - 10)/15. - Bruno Berselli, Jun 22 2012

MATHEMATICA

CoefficientList[Series[(1+3*x)/((x-1)*(4*x-1)*(1+x)), {x, 0, 30}], x] (*or*) LinearRecurrence[{4, 1, -4}, {1, 7, 29}, 40] (* Vincenzo Librandi, Jun 22 2012 *)

PROG

(MAGMA) I:=[1, 7, 29]; [n le 3 select I[n] else 4*Self(n-1)+Self(n-2)-4*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 22 2012

(PARI) x='x+O('x^99); Vec(x*(1+3*x)/((1-x)*(1-4*x)*(1+x))) \\ Altug Alkan, Sep 21 2018

CROSSREFS

Cf. A265688 (binary), A118111.

Sequence in context: A118171 A072261 A066744 * A327587 A055427 A048876

Adjacent sequences:  A037573 A037574 A037575 * A037577 A037578 A037579

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified October 23 06:58 EDT 2020. Contains 337964 sequences. (Running on oeis4.)