OFFSET
0,3
COMMENTS
Number of unoriented rows of length 11 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)=1056, there are 2^11=2048 oriented arrangements of two colors. Of these, 2^6=64 are achiral. That leaves (2048-64)/2=992 chiral pairs. Adding achiral and chiral, we get 1056. - Robert A. Russell, Nov 13 2018
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).
FORMULA
From G. C. Greubel, Jul 27 2016: (Start)
G.f.: x*(1 + 1044*x + 76332*x^2 + 1101420*x^3 + 4869558*x^4 + 7862124*x^5 + 4868556*x^6 + 1102068*x^7 + 76305*x^8 + 992*x^9)/(1 - x)^12.
E.g.f.: (1/2)* x *(2 + 1054*x + 28591*x^2 + 145815*x^3 + 246745*x^4 + 179488*x^5 + 63987*x^6 + 11880*x^7 + 1155*x^8 + 55*x^9 + x^10)*exp(x). (End)
From Robert A. Russell, Nov 13 2018: (Start)
G.f.: (Sum_{j=1..11} S2(11,j)*j!*x^j/(1-x)^(j+1) + Sum_{j=1..6} S2(6,j)*j!*x^j/(1-x)^(j+1)) / 2, where S2 is the Stirling subset number A008277.
G.f.: x*Sum_{k=0..10} A145882(11,k) * x^k / (1-x)^12.
E.g.f.: (Sum_{k=1..11} S2(11,k)*x^k + Sum_{k=1..6} S2(6,k)*x^k) * exp(x) / 2, where S2 is the Stirling subset number A008277.
For n>11, a(n) = Sum_{j=1..12} -binomial(j-13,j) * a(n-j). (End)
MATHEMATICA
Table[n^6*(n^5+1)/2, {n, 0, 30}] (* G. C. Greubel, Jul 27 2016 *)
PROG
(PARI) vector(30, n, n--; n^6*(1 + n^5)/2) \\ G. C. Greubel, Nov 15 2018
(Magma) [n^6*(1 + n^5)/2: n in [0..30]]; // G. C. Greubel, Nov 15 2018
(Sage) [n^6*(1 + n^5)/2 for n in range(30)] # G. C. Greubel, Nov 15 2018
(GAP) List([0..30], n -> n^6*(1 + n^5)/2); # G. C. Greubel, Nov 15 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 11 2009
STATUS
approved