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

1, 80, 3200, 85360, 1708800, 27392016, 366366080, 4206606640, 42340840960, 379634835920, 3070951360128, 22644802030320, 153524473002240, 963926974039440, 5639746542798720, 30914051605760688, 159505036253752320, 777889039669799760, 3599066875202445440, 15849971773188538480

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..10000

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 (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).

Formula

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.

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

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

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

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

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

+338423469991021775872609785375187500) for m >= 1. - Robert Israel, Jul 17 2015

Maple

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):
map(a, [$0..40]); # Robert Israel, Jul 17 2015

Prog

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

Crossrefs

Sequence in context: A324071 A017796 A035735 * A017743 A234325 A196280

Adjacent sequences: A035802 A035803 A035804 * A035806 A035807 A035808

Keyword

nonn

Author

N. J. A. Sloane, J. Serra-Sagrista (jserra(AT)ccd.uab.es)

Extensions

More terms from Michel Marcus, Jul 17 2015

Status

approved