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A245489
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a(n) = (1^n + (-2)^n + 4^n)/3.
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2
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1, 1, 7, 19, 91, 331, 1387, 5419, 21931, 87211, 349867, 1397419, 5593771, 22366891, 89483947, 357903019, 1431677611, 5726579371, 22906579627, 91625794219, 366504225451, 1466014804651, 5864063412907, 23456245263019, 93824997829291, 375299957762731
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: (1 - 2*x - 2*x^2) / ((1 - x) * (1 + 2*x) * (1 - 4*x)).
0 = 8*a(n) - 6*a(n+1) - 3*a(n+2) + a(n+3) for all n in Z.
E.g.f.: (exp(x) + exp(4*x) + exp(-2*x))/3. - G. C. Greubel, Sep 21 2019
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EXAMPLE
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G.f. = 1 + x + 7*x^2 + 19*x^3 + 91*x^4 + 331*x^5 + 1387*x^6 + 5419*x^7 + ...
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MAPLE
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MATHEMATICA
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CoefficientList[Series[(1-2x-2x^2)/((1-x)(1+2x)(1-4x)), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 25 2014 *)
LinearRecurrence[{3, 6, -8}, {1, 1, 7}, 30] (* Harvey P. Dale, Dec 04 2018 *)
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PROG
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(PARI) {a(n) = (1^n + (-2)^n + 4^n) / 3};
(PARI) {a(n) = if( n<0, 4^n, 1) * polcoeff( (1 - 2*x - 2*x^2) / ((1 - x) * (1 + 2*x) * (1 - 4*x)) + x * O(x^abs(n)), abs(n))};
(Sage) [(1 +(-2)^n +4^n)/3 for n in (0..30)] # G. C. Greubel, Sep 21 2019
(GAP) List([0..30], n-> (1 +(-2)^n +4^n)/3); # G. C. Greubel, Sep 21 2019
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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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