A177685 - OEIS

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A177685

a(n) = 6*a(n-1)-8*a(n-2) for n > 4; a(0)=603, a(1)=4731, a(2)=58834, a(3)=254204, a(4)=1032696.

603, 4731, 58834, 254204, 1032696, 4162544, 16713696, 66981824, 268181376, 1073233664, 4293950976, 17177836544, 68715411456, 274869776384, 1099495366656, 4398013988864, 17592120999936, 70368614088704

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OFFSET

0,1

COMMENTS

Related to Reverse and Add trajectory of 537 in base 2: a(n) = A077076(4*n+3)/6, i.e., one sixth of fourth quadrisection of A077076.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6, -8).

FORMULA

a(n) = 4^(n+6)-1985*2^(n-1) for n > 2.

G.f.: (603+1113*x+35272*x^2-60952*x^3-21856*x^4) / ((1-2*x)*(1-4*x)).

G.f. for the sequence starting at a(3): 4*x^3*(63551-123132*x) / ((1-2*x)*(1-4*x)).

MATHEMATICA

CoefficientList[Series[(603 + 1113 x + 35272 x^2 - 60952 x^3 - 21856 x^4)/((1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 24 2013 *)

LinearRecurrence[{6, -8}, {603, 4731, 58834, 254204, 1032696}, 20] (* Harvey P. Dale, May 26 2019 *)

PROG

(PARI) {m=18; v=concat([603, 4731, 58834, 254204, 1032696], vector(m-5)); for(n=6 , m, v[n]=6*v[n-1]-8*v[n-2]); v}

(Magma) [603, 4731, 58834] cat [4^(n+6)-1985*2^(n-1): n in [3..25]]; // Vincenzo Librandi, Sep 24 2013

CROSSREFS

Cf. A077076 (Reverse and Add trajectory of 537 in base 2), A177682, A177683, A177684.

Sequence in context: A066785 A178032 A107256 * A250907 A209550 A151626

Adjacent sequences: A177682 A177683 A177684 * A177686 A177687 A177688

KEYWORD

nonn

AUTHOR

Klaus Brockhaus, May 12 2010

STATUS

approved