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A037576
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Base 4 digits are, in order, the first n terms of the periodic sequence with initial period 1,3.
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6
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1, 7, 29, 119, 477, 1911, 7645, 30583, 122333, 489335, 1957341, 7829367, 31317469, 125269879, 501079517, 2004318071, 8017272285, 32069089143, 128276356573, 513105426295, 2052421705181, 8209686820727, 32838747282909
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OFFSET
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1,2
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LINKS
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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 linear recurrences with constant coefficients, signature (4,1,-4).
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Sequence in context: A118171 A072261 A066744 * A055427 A048876 A126394
Adjacent sequences: A037573 A037574 A037575 * A037577 A037578 A037579
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KEYWORD
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nonn,base,easy
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AUTHOR
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Clark Kimberling
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STATUS
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approved
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