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 A117451 Expansion of (1-x+x^2+x^5)/((1-x)*(1-x^5)). 3
 1, 0, 1, 1, 1, 3, 2, 3, 3, 3, 5, 4, 5, 5, 5, 7, 6, 7, 7, 7, 9, 8, 9, 9, 9, 11, 10, 11, 11, 11, 13, 12, 13, 13, 13, 15, 14, 15, 15, 15, 17, 16, 17, 17, 17, 19, 18, 19, 19, 19, 21, 20, 21, 21, 21, 23, 22, 23, 23, 23, 25, 24, 25, 25, 25, 27, 26, 27, 27, 27, 29, 28, 29, 29, 29, 31, 30, 31 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1). FORMULA a(n) = a(n-1) + a(n-5) - a(n-6). a(n) = -1 + ((5 + sqrt(5))/10)*cos(4*Pi*n/5) - sqrt(((5 - sqrt(5))/250)*sin(4*Pi*n/5) + ((5-sqrt(5))/10)*cos(2*Pi*n/5) + sqrt((5+sqrt(5))/250)*sin(2*Pi*n/5) + (2*n + 5)/5. a(n) = A117450(n) - A117450(n-1). - G. C. Greubel, Jun 03 2021 MATHEMATICA CoefficientList[Series[(1-x+x^2+x^5)/((1-x)(1-x^5)), {x, 0, 80}], x] (* or *) LinearRecurrence[{1, 0, 0, 0, 1, -1}, {1, 0, 1, 1, 1, 3}, 80] (* Harvey P. Dale, Jan 01 2016 *) PROG (MAGMA) R:=PowerSeriesRing(Integers(), 80); Coefficients(R!( (1-x+x^2+x^5)/((1-x)*(1-x^5)) )); // G. C. Greubel, Jun 03 2021 (Sage) def A117451_list(prec):     P. = PowerSeriesRing(ZZ, prec)     return P( (1-x+x^2+x^5)/((1-x)*(1-x^5)) ).list() A117451_list(80) # G. C. Greubel, Jun 03 2021 CROSSREFS Partial sums are A117450. Partial sums of A117452. Sequence in context: A205237 A086920 A182021 * A130970 A144733 A091460 Adjacent sequences:  A117448 A117449 A117450 * A117452 A117453 A117454 KEYWORD easy,nonn AUTHOR Paul Barry, Mar 16 2006 STATUS approved

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Last modified October 20 02:01 EDT 2021. Contains 348099 sequences. (Running on oeis4.)