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A035605
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Number of points of L1 norm 11 in cubic lattice Z^n.
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1
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0, 2, 44, 486, 3608, 20330, 93060, 361550, 1229360, 3742290, 10377180, 26572086, 63521352, 143027898, 305568564, 623207070, 1219605600, 2300164770, 4196289420, 7428962950, 12798246520, 21507034122
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OFFSET
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0,2
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REFERENCES
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M. Janjic and B. Petkovic, A Counting Function, arXiv preprint arXiv:1301.4550, 2013. - From N. J. A. Sloane, Feb 13 2013
J. Serra-Sagrista, Enumeration of lattice points in l_1 norm, Information Processing Letters, 76, no. 1-2 (2000), 39-44.
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LINKS
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Vincenzo Librandi, 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 (Abstract, pdf, ps).
Index to sequences with linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
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FORMULA
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a(n) = (2*n*(14175+83754*n^2+50270*n^4+7392*n^6+330*n^8+4*n^10))/155925. G.f.: 2*x*(1+x)^10/(1-x)^12. [Colin Barker, Apr 15 2012]
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MAPLE
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f := proc(d, m) local i; sum( 2^i*binomial(d, i)*binomial(m-1, i-1), i=1..min(d, m)); end; # n=dimension, m=norm
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MATHEMATICA
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CoefficientList[Series[2*x*(1+x)^10/(1-x)^12, {x, 0, 30}], x] (* Vincenzo Librandi, Apr 24 2012 *)
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PROG
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(MAGMA) [(2*n*(14175+83754*n^2+50270*n^4+7392*n^6+330*n^8+ 4*n^10))/155925: n in [0..30]]; /* or */
I:=[0, 2, 44, 486, 3608, 20330, 93060, 361550, 1229360, 3742290, 10377180, 26572086]; [n le 12 select I[n] else 12*Self(n-1)-66*Self(n-2)+220*Self(n-3)-495*Self(n-4)+792*Self(n-5)-924*Self(n-6)+792*Self(n-7)-495*Self(n-8)+220*Self(n-9)-66*Self(n-10)+12*Self(n-11)-Self(n-12): n in [1..31]]; // Vincenzo Librandi, Apr 24 2012
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CROSSREFS
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Sequence in context: A006313 A059737 A123829 * A203606 A009620 A001627
Adjacent sequences: A035602 A035603 A035604 * A035606 A035607 A035608
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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