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 A038391 Expansion of (x^3+2*x+1) / ((x-1)^4*(x^2+x+1)^2). 1
 1, 4, 7, 13, 23, 33, 48, 69, 90, 118, 154, 190, 235, 290, 345, 411, 489, 567, 658, 763, 868, 988, 1124, 1260, 1413, 1584, 1755, 1945, 2155, 2365, 2596, 2849, 3102, 3378, 3678, 3978, 4303, 4654, 5005, 5383, 5789, 6195, 6630, 7095, 7560, 8056, 8584, 9112, 9673 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Old Name was: Bisection of A028289. REFERENCES B. N. Cyvin et al., Enumeration of conjugated hydrocarbons..., Structural Chem., 6 (1995), 85-88, equation (8). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (2,-1,2,-4,2,-1,2,-1). FORMULA G.f.: (x^3+2*x+1) / ((x-1)^4*(x^2+x+1)^2). - Colin Barker, Aug 30 2013 From Wesley Ivan Hurt, May 07 2016: (Start) a(n) = 2*a(n-1)-a(n-2)+2*a(n-3)-4*a(n-4)+2*a(n-5)-a(n-6)+2*a(n-7)-a(n-8). a(n) = Sum_{i=1..n+1} (1+floor((n+i+1)/3)) * (1+floor((n-i+1)/3)). (End) MATHEMATICA CoefficientList[Series[(x^3 + 2 x + 1)/((x - 1)^4 (x^2 + x + 1)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 22 2013 *) LinearRecurrence[{2, -1, 2, -4, 2, -1, 2, -1}, {1, 4, 7, 13, 23, 33, 48, 69}, 50] (* Harvey P. Dale, Sep 22 2015 *) CROSSREFS Cf. A028289. Sequence in context: A316861 A298354 A139217 * A073832 A265160 A090854 Adjacent sequences:  A038388 A038389 A038390 * A038392 A038393 A038394 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Colin Barker, Aug 30 2013 Name changed by Wesley Ivan Hurt, May 07 2016 STATUS approved

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Last modified October 16 08:45 EDT 2019. Contains 328056 sequences. (Running on oeis4.)