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A035472
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Coordination sequence for lattice D*_6 (with edges defined by l_1 norm = 1).
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0
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1, 12, 72, 356, 1296, 3708, 8920, 18900, 36384, 65004, 109416, 175428, 270128, 402012, 581112, 819124, 1129536, 1527756, 2031240, 2659620, 3434832, 4381244, 5525784, 6898068, 8530528, 10458540, 12720552, 15358212, 18416496, 21943836
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OFFSET
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0,2
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REFERENCES
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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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Table of n, a(n) for n=0..29.
Index entries for linear recurrences with constant coefficients, signature (6, -15, 20, -15, 6, -1).
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FORMULA
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a(m)=add(2^k*binomial(n, k)*binomial(m-1, k-1), k=0..n)+2^n*binomial((n+2*m)/2-1, n-1); with n=6.
Conjecture: a(n)=(4*n*(31+10*n^2+4*n^4))/15. G.f.: (1+6*x+x^2)*(1+14*x^2+x^4)/(1-x)^6. [Colin Barker, Apr 14 2012]
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MATHEMATICA
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LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 12, 72, 356, 1296, 3708, 8920}, 30] (* Harvey P. Dale, Jul 03 2017 *)
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CROSSREFS
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Sequence in context: A236967 A227022 A036392 * A036398 A125322 A126480
Adjacent sequences: A035469 A035470 A035471 * A035473 A035474 A035475
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, J. Serra-Sagrista (jserra(AT)ccd.uab.es)
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STATUS
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approved
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