A035883 Coordination sequence for diamond structure D^+_14. (Edges defined by l_1 norm = 1.)

1, 0, 392, 0, 25872, 0, 703640, 8192, 10861088, 860160, 113156008, 19496960, 873656112, 222265344, 5301934776, 1666990080, 26420376640, 9372188672, 111885458888, 42600857600, 413780326736, 164317593600, 1365594249432, 555941191680, 4091822419552

Offset

0,3

Links

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 (pdf).

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 (0, 14, 0, -91, 0, 364, 0, -1001, 0, 2002, 0, -3003, 0, 3432, 0, -3003, 0, 2002, 0, -1001, 0, 364, 0, -91, 0, 14, 0, -1).

Formula

G.f.: (x^28 +378*x^26 +20475*x^24 +376740*x^22 +8192*x^21 +3222793*x^20 +745472*x^19 +16104998*x^18 +8200192*x^17 +46822139*x^16 +24600576*x^15 +68231544*x^14 +24600576*x^13 +46822139*x^12 +8200192*x^11 +16104998*x^10 +745472*x^9 +3222793*x^8 +8192*x^7 +376740*x^6 +20475*x^4 +378*x^2 +1) / ((x -1)^14*(x +1)^14). [Colin Barker, Feb 26 2013]

Maple

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=14.

Mathematica

CoefficientList[Series[(x^28 + 378 x^26 + 20475 x^24 + 376740 x^22 + 8192 x^21 + 3222793 x^20 + 745472 x^19 + 16104998 x^18 + 8200192 x^17 + 46822139 x^16 + 24600576 x^15 + 68231544 x^14 + 24600576 x^13 + 46822139 x^12 + 8200192 x^11 + 16104998 x^10 + 745472 x^9 + 3222793 x^8 + 8192 x^7 + 376740 x^6 + 20475 x^4 + 378 x^2 + 1)/((x - 1)^14 (x + 1)^14), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 21 2013 *)

Prog

(PARI) {A035883_vec(N, c=[1, 0, 378, 0, 20475, 0, 376740, 8192, 3222793, 745472, 16104998, 8200192, 46822139, 24600576, 68231544])= Vec(Pol(concat(c, vecextract(c, "-2..1")))/(x^2-1)^14+O(x^N))} \\ M. F. Hasler, Oct 21 2013

Crossrefs

Sequence in context: A264448 A160184 A187724 * A235188 A248022 A261379

Adjacent sequences: A035880 A035881 A035882 * A035884 A035885 A035886

Keyword

nonn,easy

Author

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

Extensions

Recomputed by N. J. A. Sloane, Nov 27 1998

More terms from Colin Barker, Feb 26 2013

Status

approved