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 A086926 Product of Fibonacci and (shifted) triangular numbers. 2
 0, 0, 1, 6, 18, 50, 120, 273, 588, 1224, 2475, 4895, 9504, 18174, 34307, 64050, 118440, 217192, 395352, 714951, 1285350, 2298660, 4091241, 7250221, 12797568, 22507500, 39452725, 68942718, 120132558, 208776974, 361937400, 626015085, 1080441264 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,0,-5,0,3,1). FORMULA From Franklin T. Adams-Watters, Feb 03 2006: (Start) a(n) = A000045(n)*A000217(n-1) = A000045(n)*n*(n-1)/2. a(n) = (n/(n-2)*a(n-1) + n*(n-1))/((n-2)*(n-3))*a(n-2). G.f.: x^2*(1+3x+x^3)/(1-x-x^2)^3. (End) a(n) = Sum_{k=0..n-1} Sum_{i=0..n-1} i * C(n-k-1,k). - Wesley Ivan Hurt, Sep 19 2017 From Colin Barker, Sep 20 2017: (Start) a(n) = ((-1)*(2^(-1-n)*((1-sqrt(5))^n - (1+sqrt(5))^n)*(-1+n)*n)) / sqrt(5). a(n) = 3*a(n-1) - 5*a(n-3) + 3*a(n-5) + a(n-6) for n>5. (End) MATHEMATICA Array[Fibonacci[#] PolygonalNumber[# - 1] &, 33, 0] (* or *) LinearRecurrence[{3, 0, -5, 0, 3, 1}, {0, 0, 1, 6, 18, 50}, 33] (* or *) CoefficientList[Series[x^2*(1 + 3 x + x^3)/(1 - x - x^2)^3, {x, 0, 32}], x] (* Michael De Vlieger, Dec 17 2017 *) PROG (MuPAD) numlib::fibonacci(n)*binomial(n, 2) \$ n = 0..35; // Zerinvary Lajos, May 09 2008 (PARI) concat(vector(2), Vec(x^2*(1 + 3*x + x^3) / (1 - x - x^2)^3 + O(x^40))) \\ Colin Barker, Sep 20 2017 CROSSREFS Cf. A000045, A000217, A045925. Sequence in context: A099857 A163765 A179754 * A328534 A003290 A318160 Adjacent sequences:  A086923 A086924 A086925 * A086927 A086928 A086929 KEYWORD nonn,easy AUTHOR James FitzSimons (cherry(AT)getnet.net), Sep 20 2003 EXTENSIONS Definition and more terms from Franklin T. Adams-Watters, Feb 03 2006 STATUS approved

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Last modified August 4 03:57 EDT 2021. Contains 346442 sequences. (Running on oeis4.)