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A035881
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Coordination sequence for diamond structure D^+_10. (Edges defined by l_1 norm = 1.)
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2
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1, 0, 200, 0, 6800, 512, 103000, 28160, 935200, 366080, 5805032, 2562560, 27135920, 12446720, 102442360, 47297536, 328075840, 150492160, 922953480, 418401280, 2339194064, 1046003200, 5442091160, 2399654400, 11788144480, 5127682560, 24036948520, 10321958400
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OFFSET
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0,3
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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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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 (0,10,0,-45,0,120,0,-210,0,252,0,-210,0,120,0,-45,0,10,0,-1).
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FORMULA
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G.f.: (x^20 +190*x^18 +4845*x^16 +512*x^15 +43880*x^14 +23040*x^13 +187410*x^12 +107520*x^11 +313780*x^10 +107520*x^9 +187410*x^8 +23040*x^7 +43880*x^6 +512*x^5 +4845*x^4 +190*x^2 +1) / (( x -1)^10*( x +1)^10). [Colin Barker, Nov 20 2012]
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MAPLE
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f := proc(m) local k, t1; t1 := 2^(n-1)*binomial((n+2*m)/2-1, n-1); if m mod 2 = 0 then t1 := t1+add(2^k*binomial(n, k)*binomial(m-1, k-1), k=0..n); fi; t1; end; where n=10.
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MATHEMATICA
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f[m_, n_] := 2^(n-1)*Binomial[(n+2*m)/2-1, n-1] + If[EvenQ[m], 2 *n* Hypergeometric2F1[1-m, 1-n, 2, 2], 0]; f[0, _] = 1; Table[f[m, 10], {m, 0, 22}] (* Jean-François Alcover, Apr 18 2013, after Maple *)
CoefficientList[Series[(x^20 + 190 x^18 + 4845 x^16 + 512 x^15 + 43880 x^14 + 23040 x^13 + 187410 x^12 + 107520 x^11 + 313780 x^10 + 107520 x^9 + 187410 x^8 + 23040 x^7 + 43880 x^6 + 512 x^5 + 4845 x^4 + 190 x^2 + 1)/((x - 1)^10 (x + 1)^10), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 21 2013 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Joan Serra-Sagrista (jserra(AT)ccd.uab.es)
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EXTENSIONS
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STATUS
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approved
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