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A008922
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Crystal ball sequence for lattice {E_7}*.
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1
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1, 57, 995, 8683, 48429, 198677, 653791, 1825719, 4494329, 10016209, 20601723, 39670115, 72292453, 125732205, 210093239, 339085039, 530914929, 809317097, 1204728211, 1755619419, 2509994525, 3527064133, 4879105551, 6653518247, 8955084649, 11908446081, 15660803627, 20384853715
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OFFSET
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0,2
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LINKS
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J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
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FORMULA
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G.f.: (1+x)*(1 +48*x +519*x^2 +1744*x^3 +1959*x^4 +624*x^5 +x^6)/(1-x)^8.
a(n) = (35 +37*n +679*n^2 +3928*n^3 +280*n^4 +518*n^5 -14*n^6 +68*n^7)/35.
E.g.f.: (35 +1960*x +154358x^2 +34230*x^3 +28350*x^4 +9828*x^5 +1414*x^6 +68*x^7)*exp(x)/35. (End)
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MAPLE
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seq((35 +37*n +679*n^2 +392*n^3 +280*n^4 +518*n^5 -14*n^6 +68*n^7)/35, n=0..30); # G. C. Greubel, Sep 13 2019
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MATHEMATICA
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CoefficientList[Series[(1+x)(x^6+624x^5+1959x^4+1744x^3+519x^2+48x+1)/ (1-x)^8, {x, 0, 30}], x] (* Harvey P. Dale, May 14 2019 *)
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PROG
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(PARI) a(n)=([0, 1, 0, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0, 0; 0, 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 0, 1; -1, 8, -28, 56, -70, 56, -28, 8]^n*[1; 57; 995; 8683; 48429; 198677; 653791; 1825719])[1, 1] \\ Charles R Greathouse IV, Feb 10 2017
(PARI) vector(30, n, m=n-1; (35 +37*m +679*m^2 +392*m^3 +280*m^4 +518*m^5 -14*m^6 +68*m^7)/35) \\ G. C. Greubel, Sep 13 2019
(Magma) [(35 +37*n +679*n^2 +392*n^3 +280*n^4 +518*n^5 -14*n^6 +68*n^7)/35: n in [0..30]]; // G. C. Greubel, Sep 13 2019
(Sage) [(35 +37*n +679*n^2 +392*n^3 +280*n^4 +518*n^5 -14*n^6 +68*n^7)/35 for n in (0..30)] # G. C. Greubel, Sep 13 2019
(GAP) List([0..30], n-> (35 +37*n +679*n^2 +392*n^3 +280*n^4 +518*n^5 -14*n^6 +68*n^7)/35); # G. C. Greubel, Sep 13 2019
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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STATUS
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approved
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