|
| |
|
|
A035471
|
|
Coordination sequence for lattice D*_4 (with edges defined by l_1 norm = 1).
|
|
1
|
|
|
|
1, 8, 48, 152, 352, 680, 1168, 1848, 2752, 3912, 5360, 7128, 9248, 11752, 14672, 18040, 21888, 26248, 31152, 36632, 42720, 49448, 56848, 64952, 73792, 83400, 93808, 105048, 117152, 130152, 144080
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
REFERENCES
|
J. Serra-Sagrista, Enumeration of lattice points in l_1 norm, Information Processing Letters, 76, no. 1-2 (2000), 39-44.
|
|
|
LINKS
|
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-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=4.
(16n^3 + 8n)/3, n>0.
G.f.: (1+4*x+22*x^2+4*x^3+x^4)/(1-x)^4. [Colin Barker, Apr 14 2012]
a(0)=1, a(1)=8, a(2)=48, a(3)=152, a(4)=352, a(n)=4*a(n-1)- 6*a(n-2)+ 4*a(n-3)- a(n-4). - Harvey P. Dale, Oct 20 2015
|
|
|
MATHEMATICA
|
CoefficientList[Series[(1+4*x+22*x^2+4*x^3+x^4)/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 22 2012 *)
LinearRecurrence[{4, -6, 4, -1}, {1, 8, 48, 152, 352}, 40] (* Harvey P. Dale, Oct 20 2015 *)
|
|
|
PROG
|
(MAGMA) [1] cat[(16*n^3 + 8*n)/3: n in [1..40]]; // Vincenzo Librandi, Apr 22 2012
|
|
|
CROSSREFS
|
Sequence in context: A168012 A222816 A280056 * A209443 A072819 A190317
Adjacent sequences: A035468 A035469 A035470 * A035472 A035473 A035474
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
N. J. A. Sloane, J. Serra-Sagrista (jserra(AT)ccd.uab.es)
|
|
|
STATUS
|
approved
|
| |
|
|
