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A170801 a(n) = n^10*(n^9 + 1)/2. 8
0, 1, 262656, 581160258, 137439477760, 9536748046875, 304679900238336, 5699447733924196, 72057594574798848, 675425860579888245, 5000000005000000000, 30579545237175985446, 159739999716270145536 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Number of unoriented rows of length 19 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)=262656, there are 2^19=524288 oriented arrangements of two colors. Of these, 2^10=1024 are achiral. That leaves (524288-1024)/2=261632 chiral pairs. Adding achiral and chiral, we get 262656. - Robert A. Russell, Nov 13 2018
LINKS
Index entries for linear recurrences with constant coefficients, signature (20, -190, 1140, -4845, 15504, -38760, 77520, -125970, 167960, -184756, 167960, -125970, 77520, -38760, 15504, -4845, 1140, -190, 20, -1).
FORMULA
From Robert A. Russell, Nov 13 2018: (Start)
a(n) = (A010807(n) + A008454(n)) / 2 = (n^19 + n^10) / 2.
G.f.: (Sum_{j=1..19} S2(19,j)*j!*x^j/(1-x)^(j+1) + Sum_{j=1..10} S2(10,j)*j!*x^j/(1-x)^(j+1)) / 2, where S2 is the Stirling subset number A008277.
G.f.: x*Sum_{k=0..18} A145882(19,k) * x^k / (1-x)^20.
E.g.f.: (Sum_{k=1..19} S2(19,k)*x^k + Sum_{k=1..10} S2(10,k)*x^k) * exp(x) / 2, where S2 is the Stirling subset number A008277.
For n>19, a(n) = Sum_{j=1..20} -binomial(j-21,j) * a(n-j). (End)
MAPLE
seq(n^10*(n^9 +1)/2, n=0..20); # G. C. Greubel, Oct 11 2019
MATHEMATICA
Table[(n^19 + n^10)/2, {n, 0, 30}] (* Robert A. Russell, Nov 13 2018 *)
PROG
(Magma)[n^10*(n^9+1)/2: n in [0..20]]; // Vincenzo Librandi, Aug 27 2011
(PARI) vector(30, n, n--; n^10*(n^9+1)/2) \\ G. C. Greubel, Nov 15 2018
(Sage) [n^10*(n^9+1)/2 for n in range(30)] # G. C. Greubel, Nov 15 2018
(GAP) List([0..30], n -> n^10*(n^9+1)/2); # G. C. Greubel, Nov 15 2018
CROSSREFS
Row 19 of A277504.
Cf. A010807 (oriented), A008454 (achiral).
Sequences of the form n^10*(n^m + 1)/2: A170793 (m=1), A170794 (m=2), A170795 (m=3), A170896 (m=4), A170797 (m=5), A170798 (m=6), A170799 (m=7), A170800 (m=8), this sequence (m=9), A170802 (m=10).
Sequence in context: A013966 A036096 A170792 * A340907 A253846 A253839
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 11 2009
STATUS
approved

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Last modified June 24 09:52 EDT 2024. Contains 373674 sequences. (Running on oeis4.)