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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 COMMENTS Partial sums of A255465. - Klaus Purath, Mar 18 2021 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) = (7*4^n + 3*(-1)^n - 10)/15. - Bruno Berselli, Jun 22 2012, corrected by Klaus Purath, Mar 18 2021. a(n) = floor(7*4^n/15). - Karl V. Keller, Jr., Mar 09 2021 From Klaus Purath, Mar 18 2021: (Start) a(n) = 16*a(n-2) - 3*(-1)^n + 10, assuming that a(0) = 0. a(n) = 4*a(n-1) + 2 + (-1)^n. a(n) = 5*a(n-1) - 4*a(n-2) + 2*(-1)^n, n > 2. (End) 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) my(x='x+O('x^99)); Vec(x*(1+3*x)/((1-x)*(1-4*x)*(1+x))) \\ Altug Alkan, Sep 21 2018 (Python) print([7*4**n//15 for n in range(1, 30)]) # Karl V. Keller, Jr., Mar 09 2021 CROSSREFS Cf. A007090 (numbers in base 4), A037582 (decimal), 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 September 7 22:13 EDT 2024. Contains 375749 sequences. (Running on oeis4.)