OFFSET
0,2
COMMENTS
Coordination sequence for 12-dimensional cyclotomic lattice Z[zeta_13].
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
M. Beck and S. Hosten, Cyclotomic polytopes and growth series of cyclotomic lattices, arXiv:math/0508136 [math.CO], 2005-2006.
Milan Janjic, Two Enumerative Functions
Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
FORMULA
From Colin Barker, Jan 06 2017: (Start)
a(n) = 13*n*(19056960 + 18128396*n^2 + 2641925*n^4 + 88803*n^6 + 715*n^8 + n^10)/39916800 for n>0.
G.f.: (1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + x^12) / (1 - x)^12. (End)
E.g.f.: 1 + x*(518918400 +1297296000*x +1470268800*x^2 +821620800*x^3 + 263783520*x^4 +51171120*x^5 +6280560*x^6 +489060*x^7 +24310*x^8 + 715*x^9 +13*x^10)*exp(x)/39916800. - G. C. Greubel, Nov 07 2019
MAPLE
1, seq(13*n*(19056960 + 18128396*n^2 + 2641925*n^4 + 88803*n^6 + 715*n^8 + n^10)/39916800, n=1..40); # G. C. Greubel, Nov 07 2019
MATHEMATICA
CoefficientList[(1-x^13)/(1-x)^13 + O[x]^30, x] (* Jean-François Alcover, Jan 09 2019 *)
Table[If[n==0, 1, 13*n*(19056960 + 18128396*n^2 + 2641925*n^4 + 88803*n^6 + 715*n^8 + n^10)/39916800], {n, 0, 40}] (* G. C. Greubel, Nov 07 2019 *)
PROG
(PARI) Vec((1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + x^12) / (1 - x)^12 + O(x^30)) \\ Colin Barker, Jan 06 2017
(Magma) [1] cat [13*n*(19056960 + 18128396*n^2 + 2641925*n^4 + 88803*n^6 + 715*n^8 + n^10)/39916800: n in [1..40]]; // G. C. Greubel, Nov 07 2019
(Sage) [1]+[13*n*(19056960 + 18128396*n^2 + 2641925*n^4 + 88803*n^6 + 715*n^8 + n^10)/39916800 for n in (1..40)] # G. C. Greubel, Nov 07 2019
(GAP) Concatenation([1], List([1..40], n-> 13*n*(19056960 + 18128396*n^2 + 2641925*n^4 + 88803*n^6 + 715*n^8 + n^10)/39916800 )); # G. C. Greubel, Nov 07 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved