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A177420
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a(n) = 6*a(n-1)-8*a(n-2) for n > 10; a(0)=221, a(1)=2754, a(2)=12456, a(3)=77697, a(4)=589869, a(5)=5333271, a(6)=48222198, a(7)=218509695, a(8)=3071851356, a(9)=12683673552, a(10)=51137150880.
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5
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221, 2754, 12456, 77697, 589869, 5333271, 48222198, 218509695, 3071851356, 12683673552, 51137150880, 205353516864, 823023894144, 3295315229952, 13187700226560, 52763679519744, 211080475305984, 844373415677952
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OFFSET
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0,1
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COMMENTS
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Related to Reverse and Add trajectory of 442 in base 2: a(n) = A075268(4*n)/2, i.e. one half of first quadrisection of A075268.
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LINKS
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FORMULA
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a(n) = 3*4^(n+7)-12576771*2^(n-5) for n > 8.
G.f.: (221+1428*x-2300*x^2+24993*x^3+223335*x^4+2415633*x^5 +20941524*x^6-28157325*x^7+2146570770*x^8-3999357024*x^9-390079584*x^10) / ((1-2*x)*(1-4*x)).
G.f. for the sequence starting at a(9): 48*x^9*(264243199-520101884*x) / ((1-2*x)*(1-4*x)).
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MATHEMATICA
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CoefficientList[Series[(221 + 1428 x - 2300 x^2 + 24993 x^3 + 223335 x^4 + 2415633 x^5 + 20941524 x^6 - 28157325 x^7 + 2146570770 x^8 - 3999357024 x^9 - 390079584 x^10)/((1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 24 2013 *)
LinearRecurrence[{6, -8}, {221, 2754, 12456, 77697, 589869, 5333271, 48222198, 218509695, 3071851356, 12683673552, 51137150880}, 20] (* Harvey P. Dale, Nov 02 2020 *)
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PROG
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(PARI) {m=18; v=concat([221, 2754, 12456, 77697, 589869, 5333271, 48222198, 218509695, 3071851356, 12683673552, 51137150880], vector(m-11)); for(n=12, m, v[n]=6*v[n-1]-8*v[n-2]); v}
(Magma) [221, 2754, 12456, 77697, 589869, 5333271, 48222198, 218509695, 3071851356] cat [3*4^(n+7)-12576771*2^(n-5): n in [9..25]]; // Vincenzo Librandi, Sep 24 2013
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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