OFFSET
0,3
COMMENTS
By definition, all terms are triangular numbers. - Harvey P. Dale, Aug 12 2012
Number of unoriented rows of length 20 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)=524800, there are 2^20=1048576 oriented arrangements of two colors. Of these, 2^10=1024 are achiral. That leaves (1048576-1024)/2=523776 chiral pairs. Adding achiral and chiral, we get 524800. - 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 (21, -210, 1330, -5985, 20349, -54264, 116280, -203490, 293930, -352716, 352716, -293930, 203490, -116280, 54264, -20349, 5985, -1330, 210, -21, 1).
FORMULA
From Robert A. Russell, Nov 13 2018: (Start)
G.f.: (Sum_{j=1..20} S2(20,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..19} A145882(20,k) * x^k / (1-x)^21.
E.g.f.: (Sum_{k=1..20} S2(20,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>20, a(n) = Sum_{j=1..21} -binomial(j-22,j) * a(n-j). (End)
MAPLE
seq(n^10*(n^10 +1)/2, n=0..20); # G. C. Greubel, Oct 11 2019
MATHEMATICA
n10[n_]:=Module[{c=n^10}, (c(c+1))/2]; Array[n10, 15, 0] (* Harvey P. Dale, Jul 17 2012 *)
PROG
(Magma) [n^10*(n^10+1)/2: n in [0..20]]; // Vincenzo Librandi, Aug 27 2011
(PARI) vector(30, n, n--; n^10*(n^10+1)/2) \\ G. C. Greubel, Nov 15 2018
(Sage) [n^10*(n^10+1)/2 for n in range(30)] # G. C. Greubel, Nov 15 2018
(GAP) List([0..30], n -> n^10*(n^10+1)/2); # G. C. Greubel, Nov 15 2018
(Python) for n in range(0, 20): print(int(n**10*(n**10 + 1)/2), end=', ') # Stefano Spezia, Nov 15 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 11 2009
STATUS
approved