A035729 Coordination sequence for 34-dimensional cubic lattice.

1, 68, 2312, 52428, 892432, 12168532, 138504984, 1354168796, 11614313504, 88805833316, 613171117352, 3863171679980, 22402282117680, 120450005575540, 604244840324920, 2843633280971772, 12614155679414336, 52965710906750084, 211305268473868616

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

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 (34, -561, 5984, -46376, 278256, -1344904, 5379616, -18156204, 52451256, -131128140, 286097760, -548354040, 927983760, -1391975640, 1855967520, -2203961430, 2333606220, -2203961430, 1855967520, -1391975640, 927983760, -548354040, 286097760, -131128140, 52451256, -18156204, 5379616, -1344904, 278256, -46376, 5984, -561, 34, -1).

Formula

G.f.: ((1+x)/(1-x))^34. [clarified by Harvey P. Dale, Dec 07 2014]

n*a(n) = 68*a(n-1) + (n-2)*a(n-2) for n > 1. - Seiichi Manyama, Aug 24 2018

Maple

seq(coeff(series(((1+x)/(1-x))^34, x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Aug 24 2018

Mathematica

CoefficientList[Series[((1+x)/(1-x))^34, {x, 0, 20}], x] (* Harvey P. Dale, Dec 07 2014 *)

Prog

(GAP) a:=[1, 68];; for n in [3..20] do a[n]:=1/(n-1)*(68*a[n-1]+(n-3)*a[n-2]); od; a; # Muniru A Asiru, Aug 24 2018
(PARI) x='x+O('x^25); Vec(((1+x)/(1-x))^34) \\ Altug Alkan, Aug 24 2018
(Magma) I:=[1, 68]; [n le 2 select I[n] else 1/(n-1)*(68*Self(n-1)+(n-3)*Self(n-2)): n in [1..30]]; // Vincenzo Librandi, Aug 29 2018

Crossrefs

Sequence in context: A220722 A017784 A035802 * A017731 A204298 A281556

Adjacent sequences: A035726 A035727 A035728 * A035730 A035731 A035732

Keyword

nonn,easy

Author

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

Extensions

Recomputed by N. J. A. Sloane, Nov 25 1998

Status

approved