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A035805 Coordination sequence for lattice D*_40 (with edges defined by l_1 norm = 1). 1

%I #16 Jan 24 2016 12:10:05

%S 1,80,3200,85360,1708800,27392016,366366080,4206606640,42340840960,

%T 379634835920,3070951360128,22644802030320,153524473002240,

%U 963926974039440,5639746542798720,30914051605760688,159505036253752320,777889039669799760,3599066875202445440,15849971773188538480

%N Coordination sequence for lattice D*_40 (with edges defined by l_1 norm = 1).

%H Robert Israel, <a href="/A035805/b035805.txt">Table of n, a(n) for n = 0..10000</a>

%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.

%H <a href="/index/Rec#order_40">Index entries for linear recurrences with constant coefficients</a>, signature (40, -780, 9880, -91390, 658008, -3838380, 18643560, -76904685, 273438880, -847660528, 2311801440, -5586853480, 12033222880, -23206929840, 40225345056, -62852101650, 88732378800, -113380261800, 131282408400, -137846528820, 131282408400, -113380261800, 88732378800, -62852101650, 40225345056, -23206929840, 12033222880, -5586853480, 2311801440, -847660528, 273438880, -76904685, 18643560, -3838380, 658008, -91390, 9880, -780, 40, -1).

%F a(m) = add(2^k*binomial(n, k)*binomial(m-1, k-1), k=0..n)+2^n*binomial((n+2*m)/2-1, n-1); with n=40.

%F a(m) = (16/593656501767616816756789390344140625)*m*(4*m^38+4940*m^36+26704158*m^34+22285268720*m^32+22169269111132*m^30+10351928397671640*m^28+

%F 4172063382329354916*m^26+1038965255065355030400*m^24+201893761151519264993880*m^22+26199472654360125659009900*m^20

%F +2524128772403346489496391926*m^18+163210735760625747200765141760*m^16+7467789811143426643831718047372*m^14

%F +220080762455391115171018307605280*m^12+4279184659378901865138986667818448*m^10+48505704323330204055616545034472160*m^8

%F +319916777166545405366489956014502539*m^6+974191638722297841470545251258107700*m^4+1282738019661976478019433674496278750*m^2

%F +338423469991021775872609785375187500) for m >= 1. - _Robert Israel_, Jul 17 2015

%p a:= m -> add(2^k*binomial(40, k)*binomial(m-1, k-1), k=0..40)+2^40*binomial((40+2*m)/2-1, 40-1):

%p map(a, [$0..40]); # _Robert Israel_, Jul 17 2015

%o (PARI) mybinom(x,y) = if ((x==-1) && (y==-1), 1, binomial(x,y));

%o a(m, n=40) = sum(k=0, n, 2^k*mybinom(n, k)*mybinom(m-1, k-1))+2^n*mybinom((n+2*m)/2-1, n-1); \\ _Michel Marcus_, Jul 17 2015

%K nonn

%O 0,2

%A _N. J. A. Sloane_, J. Serra-Sagrista (jserra(AT)ccd.uab.es)

%E More terms from _Michel Marcus_, Jul 17 2015

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)