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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
OFFSET
0,2
LINKS
Joan Serra-Sagrista, Enumeration of lattice points in l_1 norm, Inf. Proc. Lett. 76 (1-2) (2000) 39-44.
FORMULA
a(m) = (Sum_{k=0..n} 2^k*binomial(n, k)*binomial(m-1, k-1)) + 2^n * binomial((n+2*m)/2-1, n-1); with n=4.
a(n) = (16*n^3 + 8*n)/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(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=1, a(1)=8, a(2)=48, a(3)=152, a(4)=352. - Harvey P. Dale, Oct 20 2015
For n >= 1, a(n) = 8*n + 32*Sum_{k=0..n-1} (k*n - k^2). - Christopher Hohl, Apr 12 2019
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, J. Serra-Sagrista (jserra(AT)ccd.uab.es)
STATUS
approved