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A035729
Coordination sequence for 34-dimensional cubic lattice.
3
1, 68, 2312, 52428, 892432, 12168532, 138504984, 1354168796, 11614313504, 88805833316, 613171117352, 3863171679980, 22402282117680, 120450005575540, 604244840324920, 2843633280971772, 12614155679414336, 52965710906750084, 211305268473868616
OFFSET
0,2
LINKS
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
KEYWORD
nonn,easy
AUTHOR
Joan Serra-Sagrista (jserra(AT)ccd.uab.es)
EXTENSIONS
Recomputed by N. J. A. Sloane, Nov 25 1998
STATUS
approved