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A045651 L1-coordination sequence for E_8 lattice in Construction A version of the lattice. 1
1, 16, 128, 688, 2944, 10448, 31616, 83824, 199424, 434064, 877696, 1668656, 3011200, 5196880, 8630144, 13858544, 21607936, 32823056, 48713856, 70807984, 101009792, 141666256, 195640192, 266391152, 358064384, 475588240, 624780416, 812463408, 1046589568 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Joan Serra-Sagrista, Enumeration of lattice points in l_1 norm, Inf. Proc. Lett. 76 (1-2) (2000) 39-44.

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

FORMULA

[ Sum_{i=1..min(8, n)} 2^8 * C(8, i) * C(n-1, i-1) ] + [ 2^(8-1)*C((((8+2n)/2)-1), 8-1) ].

G.f.: (x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 198*x^4 + 56*x^3 + 28*x^2 + 8*x + 1) / (x-1)^8. - Colin Barker, Mar 04 2015

PROG

(PARI) Vec((x^8+8*x^7+28*x^6+56*x^5+198*x^4+56*x^3+28*x^2+8*x+1)/(x-1)^8 + O(x^100)) \\ Colin Barker, Mar 04 2015

CROSSREFS

Sequence in context: A290031 A008535 A008416 * A035473 A014972 A115977

Adjacent sequences:  A045648 A045649 A045650 * A045652 A045653 A045654

KEYWORD

easy,nonn

AUTHOR

Joan Serra-Sagrista (jserra(AT)ccd.uab.es)

STATUS

approved

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Last modified March 23 14:17 EDT 2019. Contains 321431 sequences. (Running on oeis4.)