# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a035805 Showing 1-1 of 1 %I A035805 #16 Jan 24 2016 12:10:05 %S A035805 1,80,3200,85360,1708800,27392016,366366080,4206606640,42340840960, %T A035805 379634835920,3070951360128,22644802030320,153524473002240, %U A035805 963926974039440,5639746542798720,30914051605760688,159505036253752320,777889039669799760,3599066875202445440,15849971773188538480 %N A035805 Coordination sequence for lattice D*_40 (with edges defined by l_1 norm = 1). %H A035805 Robert Israel, Table of n, a(n) for n = 0..10000 %H A035805 Joan Serra-Sagrista, Enumeration of lattice points in l_1 norm, Inf. Proc. Lett. 76 (1-2) (2000) 39-44. %H A035805 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). %F A035805 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 A035805 a(m) = (16/593656501767616816756789390344140625)*m*(4*m^38+4940*m^36+26704158*m^34+22285268720*m^32+22169269111132*m^30+10351928397671640*m^28+ %F A035805 4172063382329354916*m^26+1038965255065355030400*m^24+201893761151519264993880*m^22+26199472654360125659009900*m^20 %F A035805 +2524128772403346489496391926*m^18+163210735760625747200765141760*m^16+7467789811143426643831718047372*m^14 %F A035805 +220080762455391115171018307605280*m^12+4279184659378901865138986667818448*m^10+48505704323330204055616545034472160*m^8 %F A035805 +319916777166545405366489956014502539*m^6+974191638722297841470545251258107700*m^4+1282738019661976478019433674496278750*m^2 %F A035805 +338423469991021775872609785375187500) for m >= 1. - _Robert Israel_, Jul 17 2015 %p A035805 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 A035805 map(a, [$0..40]); # _Robert Israel_, Jul 17 2015 %o A035805 (PARI) mybinom(x,y) = if ((x==-1) && (y==-1), 1, binomial(x,y)); %o A035805 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 A035805 nonn %O A035805 0,2 %A A035805 _N. J. A. Sloane_, J. Serra-Sagrista (jserra(AT)ccd.uab.es) %E A035805 More terms from _Michel Marcus_, Jul 17 2015 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE