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A228472 a(n) = 6*a(n-2) + a(n-4), where a(0) = 5, a(1) = 8, a(2) = 30, a(3) = 49. 1
5, 8, 30, 49, 185, 302, 1140, 1861, 7025, 11468, 43290, 70669, 266765, 435482, 1643880, 2683561, 10130045, 16536848, 62424150, 101904649, 384674945, 627964742, 2370473820, 3869693101, 14607517865, 23846123348, 90015581010, 146946433189, 554701003925 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Let d = A228471.  Then a(n) is the least k > d(n) such that trace(k/d(n)) consists of the first n terms of 10101010101010101...   See A228470.

LINKS

Clark Kimberling, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,6,0,1).

FORMULA

a(n) = (3+sqrt(10))^(1/4*((-1)^n-1)+1/2*n)*(13/4+sqrt(10)*(1-1/4*(-1)^n) -3/4*(-1)^n)+(3-sqrt(10))^(1/4*((-1)^n-1)+1/2*n)*(13/4-sqrt(10)*(1-1/4*(-1)^n) -3/4*(-1)^n). - Paolo P. Lava, Sep 12 2013

EXAMPLE

See A228471.

MAPLE

P:=proc(q) local n; for n from 0 to q do print(evalf((3+sqrt(10))^(1/4*((-1)^n-1)+1/2*n)*(13/4+sqrt(10)*(1-1/4*(-1)^n) -3/4*(-1)^n)+(3-sqrt(10))^(1/4*((-1)^n-1)+1/2*n)*(13/4-sqrt(10)*(1-1/4*(-1)^n) -3/4*(-1)^n))); od; end: P(100); # Paolo P. Lava, Sep 12 2013

MATHEMATICA

c1 = CoefficientList[Series[(3 + 5 x + x^2 + x^3)/(1 - 6 x^2 - x^4), {x, 0, 40}], x]; c2 = CoefficientList[Series[(5 + 8 x + x^3)/(1 - 6 x^2 - x^4), {x, 0, 40}], x]; pairs = Transpose[CoefficientList[Series[{-((3 + 11 x + 2 x^3)/(-1 + 6 x^2 + x^4)), -((2 + 8 x + x^2 + x^3)/(-1 + 6 x^2 + x^4))}, {x, 0, 20}], x]]; t[{x_, y_, _}] := t[{x, y}]; t[{x_, y_}] := Prepend[If[# > y - #, {y - #, 1}, {#, 0}], y] &[Mod[x, y]]; userIn2[{x_, y_}] := Most[NestWhileList[t, {x, y}, (#[[2]] > 0) &]]; Map[Map[#[[3]] &, Rest[userIn2[#]]] &, pairs] (* Peter J. C. Moses, Aug 20 2013 *)

LinearRecurrence[{0, 6, 0, 1}, {5, 8, 30, 49}, 30] (* T. D. Noe, Aug 23 2013 *)

CROSSREFS

Cf. A228471, A228469.

Sequence in context: A076593 A219775 A129774 * A049373 A304647 A002536

Adjacent sequences:  A228469 A228470 A228471 * A228473 A228474 A228475

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 22 2013

STATUS

approved

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Last modified November 15 04:00 EST 2018. Contains 317225 sequences. (Running on oeis4.)