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 A008394 Crystal ball sequence for A_9 lattice. 3
 1, 91, 2161, 24691, 176251, 907753, 3685123, 12494233, 36808723, 96918753, 232834755, 518344905, 1082218305, 2139007755, 4032416505, 7294752507, 12726601437, 21501506127, 35301145037, 56487256007 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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). 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 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 *) PROG (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 */ (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 (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 CROSSREFS Sequence in context: A229518 A118706 A119150 * A332949 A221738 A332913 Adjacent sequences: A008391 A008392 A008393 * A008395 A008396 A008397 KEYWORD nonn AUTHOR N. J. A. Sloane and J. H. Conway STATUS approved

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Last modified December 2 01:41 EST 2023. Contains 367505 sequences. (Running on oeis4.)