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 A170791 a(n) = n^9*(n^9 + 1)/2. 2
 0, 1, 131328, 193720086, 34359869440, 1907349609375, 50779983373056, 814206819132028, 9007199321849856, 75047317842209805, 500000000500000000, 2779958657925089586, 13311666643022512128, 56227703481280946251 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Number of unoriented rows of length 18 using up to n colors. For a(0)=0, there are no rows using no colors. For a(1)=1, there is one row using that one color for all positions. For a(2)=131328, there are 2^18=262144 oriented arrangements of two colors. Of these, 2^9=512 are achiral. That leaves (262144-512)/2=130816 chiral pairs. Adding achiral and chiral, we get 131328. - Robert A. Russell, Nov 13 2018 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (19,-171,969,-3876,11628,-27132, 50388,-75582,92378,-92378,75582,-50388,27132,-11628,3876,-969,171, -19,1). FORMULA G.f.: (x + 131309*x^2 + 191225025*x^3 + 30701643925*x^4 + 1287510971765*x^5 + 20228672721537*x^6 + 142998536758213*x^7 + 503354983579865*x^8 + 932692830330915*x^9 + 932692827449735*x^10 + 503354984335363*x^11 + 142998537549087*x^12 + 20228672026535*x^13 + 1287511125835*x^14 + 30701669175*x^15 + 191214899*x^16 + 130816*x^17) /(1-x)^19. - G. C. Greubel, Dec 06 2017 From Robert A. Russell, Nov 13 2018: (Start) a(n) = (A010806(n) + A001017(n)) / 2 = (n^18 + n^9) / 2. G.f.: (Sum_{j=1..18} S2(18,j)*j!*x^j/(1-x)^(j+1) + Sum_{j=1..9} S2(9,j)*j!*x^j/(1-x)^(j+1)) / 2, where S2 is the Stirling subset number A008277. G.f.: x*Sum_{k=0..17} A145882(18,k) * x^k / (1-x)^19. E.g.f.: (Sum_{k=1..18} S2(18,k)*x^k + Sum_{k=1..9} S2(9,k)*x^k) * exp(x) / 2, where S2 is the Stirling subset number A008277. For n>18, a(n) = Sum_{j=1..19} -binomial(j-20,j) * a(n-j). (End) MATHEMATICA f[n_]:=Module[{n9=n^9}, (n9(n9+1))/2]; Array[f, 20, 0] (* Harvey P. Dale, Nov 24 2012 *) Table[n^9*(n^9+1)/2, {n, 0, 30}] (* G. C. Greubel, Dec 06 2017 *) PROG (Magma) [n^9*(n^9+1)/2: n in [0..20]]; // Vincenzo Librandi, Aug 26 2011 (PARI) for(n=0, 30, print1(n^9*(n^9+1)/2, ", ")) \\ G. C. Greubel, Dec 06 2017 (Sage) [n^9*(1 + n^9)/2 for n in range(30)] # G. C. Greubel, Nov 15 2018 (GAP) List([0..30], n -> n^9*(n^9 + 1)/2); # G. C. Greubel, Nov 15 2018 (Python) for n in range(0, 20): print(int(n**9*(n**9 + 1)/2), end=', ') # Stefano Spezia, Nov 15 2018 CROSSREFS Row 18 of A277504. Cf. A010806 (oriented), A001017 (achiral). Sequence in context: A234687 A170782 A237004 * A203892 A208488 A170800 Adjacent sequences: A170788 A170789 A170790 * A170792 A170793 A170794 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Dec 11 2009 STATUS approved

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Last modified July 25 00:10 EDT 2024. Contains 374585 sequences. (Running on oeis4.)