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A035604 Number of points of L1 norm 10 in cubic lattice Z^n. 3

%I

%S 0,2,40,402,2720,14002,58728,209762,658048,1854882,4780008,11414898,

%T 25534368,53972178,108568488,209070018,387328512,693230658,1202893992,

%U 2029779538,3339504032,5369283570,8453107432,13053926690,19804348032,29557550050,43450388072

%N Number of points of L1 norm 10 in cubic lattice Z^n.

%H T. D. Noe, <a href="/A035604/b035604.txt">Table of n, a(n) for n = 0..1000</a>

%H J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (<a href="http://neilsloane.com/doc/Me220.pdf">pdf</a>).

%H M. Janjic and B. Petkovic, <a href="http://arxiv.org/abs/1301.4550">A Counting Function</a>, arXiv preprint arXiv:1301.4550 [math.CO], 2013. - _N. J. A. Sloane_, Feb 13 2013

%H M. Janjic, B. Petkovic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Janjic/janjic45.html">A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers</a>, J. Int. Seq. 17 (2014) # 14.3.5.

%H Joan Serra-Sagrista, <a href="http://dx.doi.org/10.1016/S0020-0190(00)00119-8">Enumeration of lattice points in l_1 norm</a>, Inf. Proc. Lett. 76 (1-2) (2000) 39-44.

%F a(n) = 2n^2/14175 * (2n^8 + 120n^6 + 1806n^4 + 7180n^2 + 5067).

%F G.f.: 2*x*(1+x)^9/(1-x)^11. - _Colin Barker_, Apr 15 2012

%F a(n) = 2*A099197(n). - _R. J. Mathar_, Dec 10 2013

%F a(n) = a(n-1) + A035603(n) + A035603(n-1). - _Bruce J. Nicholson_, Mar 11 2018

%p 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

%t f[d_, m_] := Sum[2^i*Binomial[d, i]*Binomial[m-1, i-1], {i, 1, Min[d, m]}];

%t a[n_] := f[n, 10];

%t Table[a[n], {n, 0, 26}] (* _Jean-Fran├žois Alcover_, Nov 24 2017, from Maple *)

%o (PARI) x='x+O('x^99); concat(0, Vec(2*x*(1+x)^9/(1-x)^11)) \\ _Altug Alkan_, Mar 12 2018

%Y Cf. A035607.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

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Last modified May 20 12:33 EDT 2019. Contains 323422 sequences. (Running on oeis4.)