login
A035474
Coordination sequence for lattice D*_10 (with edges defined by l_1 norm = 1).
2
1, 20, 200, 1340, 6800, 29028, 108120, 355980, 1047840, 2793140, 6830056, 15502300, 32993200, 66410500, 127335800, 233975084, 414071360, 708767060, 1177632520, 1905107580, 3008636112, 4648808100, 7041860760, 10474929100, 15324477280, 22078385140, 31362209320
OFFSET
0,2
LINKS
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 (10, -45, 120, -210, 252, -210, 120, -45, 10, -1).
FORMULA
a(m) = sum(2^k*binomial(n, k)*binomial(m-1, k-1), k=0..n)+2^n*binomial((n+2*m)/2-1, n-1), where n=10, a(0)=1.
G.f.: (x^2+6*x+1)*(x^8+4*x^7+20*x^6-4*x^5+214*x^4-4*x^3+20*x^2+4*x+1) / (x-1)^10. [Colin Barker, Nov 19 2012]
MATHEMATICA
CoefficientList[Series[(x^2 + 6 x + 1) (x^8 + 4 x^7 + 20 x^6 - 4 x^5 + 214 x^4 - 4 x^3 + 20 x^2 + 4 x + 1)/(x - 1)^10, {x, 0, 40}], x] (* Vincenzo Librandi, Oct 21 2013 *)
LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {1, 20, 200, 1340, 6800, 29028, 108120, 355980, 1047840, 2793140, 6830056}, 30] (* Harvey P. Dale, Mar 22 2020 *)
PROG
(Magma) n:=10; [1] cat [&+[2^k*Binomial(n, k)*Binomial(m-1, k-1): k in [0..n]]+2^n*Binomial((n+2*m) div 2-1, n-1): m in [1..30]]; // Bruno Berselli, Oct 21 2013
CROSSREFS
Sequence in context: A126901 A008420 A045758 * A103261 A120796 A120787
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, J. Serra-Sagrista (jserra(AT)ccd.uab.es)
EXTENSIONS
More terms from Vincenzo Librandi, Oct 21 2013
STATUS
approved