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 A008398 Crystal ball sequence for E_7 lattice. 1
 1, 127, 3025, 28911, 162417, 652431, 2086241, 5659295, 13561889, 29504095, 59400241, 112234255, 201127185, 344628207, 568250433, 906272831, 1403829569, 2119308095, 3127077265, 4520566831 (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). Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1). Index entries for crystal ball sequences FORMULA a(n) = 1 + (2/105)*n*(222*n^6 + 756*n^5 + 1260*n^4 + 1470*n^3 + 1708*n^2 + 1029*n + 170). G.f.: (1+119*x+2037*x^2+8211*x^3+8787*x^4+2037*x^5+119*x^6+x^7)/(1-x)^8. - Colin Barker, Mar 16 2012 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8). - Harvey P. Dale, Jul 18 2012 MAPLE seq(148/35*n^7+72/5*n^6+24*n^5+28*n^4+488/15*n^3+98/5*n^2+68/21*n+1, n=0..30); MATHEMATICA Table[148/35n^7+72/5n^6+24n^5+28n^4+488/15n^3+98/5n^2+68/21n+1, {n, 0, 20}] (* or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {1, 127, 3025, 28911, 162417, 652431, 2086241, 5659295}, 20] (* Harvey P. Dale, Jul 18 2012 *) PROG (PARI) a(n)=(444*n^7 + 1512*n^6 + 2520*n^5 + 2940*n^4 + 3416*n^3 + 2058*n^2 + 340*n + 105)/105 \\ Charles R Greathouse IV, Feb 10 2017 (Magma) [1 +(2/105)*n*(222*n^6 +756*n^5 +1260*n^4 +1470*n^3 +1708*n^2 +1029*n +170): n in [0..30]]; // G. C. Greubel, May 29 2023 (SageMath) def A008398(n): return 1 +2*n*(222*n^6 +756*n^5 +1260*n^4 +1470*n^3 +1708*n^2 +1029*n +170)//105 [A008398(n) for n in range(31)] # G. C. Greubel, May 29 2023 CROSSREFS Sequence in context: A321552 A321546 A345458 * A144969 A114535 A215611 Adjacent sequences: A008395 A008396 A008397 * A008399 A008400 A008401 KEYWORD nonn,easy,nice AUTHOR N. J. A. Sloane and J. H. Conway STATUS approved

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Last modified December 2 01:36 EST 2023. Contains 367505 sequences. (Running on oeis4.)