A008394 Crystal ball sequence for A_9 lattice.
1, 91, 2161, 24691, 176251, 907753, 3685123, 12494233, 36808723, 96918753, 232834755, 518344905, 1082218305, 2139007755, 4032416505, 7294752507, 12726601437, 21501506127, 35301145037, 56487256007
Offset: 0
Keywords
Links
- T. D. Noe, Table of n, a(n) for n = 0..1000
- J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
- Daniel J. Greenhoe, Frames and Bases: Structure and Design, Version 0.20, Signal Processing ABCs series (2019) Vol. 4, see page 175.
- Daniel J. Greenhoe, A Book Concerning Transforms, Version 0.10, Signal Processing ABCs series (2019) Vol. 5, see page 97.
- Index entries for crystal ball sequences
- Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
Programs
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Magma
[(2*n+1)*(12155*n^8 +48620*n^7 +241670*n^6 +554840*n^5 +1130987*n^4 +1393964*n^3 +1276308*n^2 +663696*n +181440)/181440: n in [0..40]]; // G. C. Greubel, May 27 2023
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Mathematica
CoefficientList[Series[(1+x)(1 +80x +1216x^2 +5840x^3 +10036x^4 +5840x^5 +1216x^6 +80x^7 +x^8)/(1-x)^10, {x,0,30}], x] (* Michael De Vlieger, Mar 13 2020 *) -
Maxima
A008394(n):=2431/18144*n^9+2431/4032*n^8+4433/1512*n^7+715/96*n^6+67067/4320*n^5+4147/192*n^4+197329/9072*n^3+14465/1008*n^2+7129/1260*n+1$ makelist(A008394(n),n,0,30); /* Martin Ettl, Oct 25 2012 */
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SageMath
[(2*n+1)*(12155*n^8 +48620*n^7 +241670*n^6 +554840*n^5 +1130987*n^4 +1393964*n^3 +1276308*n^2 +663696*n +181440)/181440 for n in range(41)] # G. C. Greubel, May 27 2023
Formula
a(n) = 2431/18144*n^9 + 2431/4032*n^8 + 4433/1512*n^7 + 715/96*n^6 + 67067/4320*n^5 + 4147/192*n^4 + 197329/9072*n^3 + 14465/1008*n^2 + 7129/1260*n + 1. - T. D. Noe, Apr 29 2007
G.f.: (1+x)*(1 + 80*x + 1216*x^2 + 5840*x^3 + 10036*x^4 + 5840*x^5 + 1216*x^6 + 80*x^7 + x^8)/(1-x)^10. - Colin Barker, Mar 16 2012