A035605 Number of points of L1 norm 11 in cubic lattice Z^n.

0, 2, 44, 486, 3608, 20330, 93060, 361550, 1229360, 3742290, 10377180, 26572086, 63521352, 143027898, 305568564, 623207070, 1219605600, 2300164770, 4196289420, 7428962950, 12798246520, 21507034122

Offset

0,2

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).

M. Janjic and B. Petkovic, A Counting Function, arXiv preprint arXiv:1301.4550 [math.CO], 2013. - N. J. A. Sloane, Feb 13 2013

M. Janjic, B. Petkovic, A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers, J. Int. Seq. 17 (2014) # 14.3.5.

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 (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Formula

From Colin Barker, Apr 15 2012: (Start)

a(n) = (2*n*(14175 + 83754*n^2 + 50270*n^4 + 7392*n^6 + 330*n^8 + 4*n^10))/155925.

G.f.: 2*x*(1+x)^10/(1-x)^12. (End)

Maple

f := proc(d, m) local i; sum( 2^i*binomial(d, i)*binomial(m-1, i-1), i=1..min(d, m)); end; # n=dimension, m=norm

Mathematica

CoefficientList[Series[2*x*(1+x)^10/(1-x)^12, {x, 0, 30}], x] (* Vincenzo Librandi, Apr 24 2012 *)
LinearRecurrence[{12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1}, {0, 2, 44, 486, 3608, 20330, 93060, 361550, 1229360, 3742290, 10377180, 26572086}, 30] (* Harvey P. Dale, Dec 23 2016 *)

Prog

(Magma) [(2*n*(14175+83754*n^2+50270*n^4+7392*n^6+330*n^8+ 4*n^10))/155925: n in [0..30]]; /* or */
I:=[0, 2, 44, 486, 3608, 20330, 93060, 361550, 1229360, 3742290, 10377180, 26572086]; [n le 12 select I[n] else 12*Self(n-1)-66*Self(n-2)+220*Self(n-3)-495*Self(n-4)+792*Self(n-5)-924*Self(n-6)+792*Self(n-7)-495*Self(n-8)+220*Self(n-9)-66*Self(n-10)+12*Self(n-11)-Self(n-12): n in [1..31]]; // Vincenzo Librandi, Apr 24 2012

Crossrefs

Sequence in context: A059737 A123829 A242856 * A285746 A203606 A009620

Adjacent sequences: A035602 A035603 A035604 * A035606 A035607 A035608

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved