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A037576 Base 4 digits are, in order, the first n terms of the periodic sequence with initial period 1,3. 6
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 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

CROSSREFS

Sequence in context: A118171 A072261 A066744 * A055427 A048876 A126394

Adjacent sequences:  A037573 A037574 A037575 * A037577 A037578 A037579

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified August 28 08:35 EDT 2015. Contains 261118 sequences.