A035477 - OEIS

%I #15 Sep 05 2023 13:04:58

%S 1,32,512,5472,44032,285088,1549824,7288544,30382080,114509600,

%T 396241408,1273082976,3829072896,10848180384,29093973504,74178420192,

%U 180482027520,420523089440,941348409856,2030565262176,4232440732672,8546273961888,16756632155648

%N Coordination sequence for lattice D*_16 (with edges defined by l_1 norm = 1).

%H Colin Barker, <a href="/A035477/b035477.txt">Table of n, a(n) for n = 0..1000</a>

%H Joan Serra-Sagrista, <a href="http://dx.doi.org/10.1016/S0020-0190(00)00119-8">Enumeration of lattice points in l_1 norm</a>, Inf. Proc. Lett. 76 (1-2) (2000) 39-44.

%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (16, -120, 560, -1820, 4368, -8008, 11440, -12870, 11440, -8008, 4368, -1820, 560, -120, 16, -1).

%F 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=16.

%F G.f.: (1 +16*x +120*x^2 +560*x^3 +1820*x^4 +4368*x^5 +8008*x^6 +11440*x^7 +78406*x^8 +11440*x^9 +8008*x^10 +4368*x^11 +1820*x^12 +560*x^13 +120*x^14 +16*x^15 +x^16) / (1 -x)^16. - _Colin Barker_, Dec 23 2015

%t Table[SeriesCoefficient[(1 + 16 x + 120 x^2 + 560 x^3 + 1820 x^4 + 4368 x^5 + 8008 x^6 + 11440 x^7 + 78406 x^8 + 11440 x^9 + 8008 x^10 + 4368 x^11 + 1820 x^12 + 560 x^13 + 120 x^14 + 16 x^15 + x^16)/(1 - x)^16, {x, 0, n}], {n, 0, 22}] (* _Michael De Vlieger_, Dec 23 2015 *)

%o (PARI) Vec((1 +16*x +120*x^2 +560*x^3 +1820*x^4 +4368*x^5 +8008*x^6 +11440*x^7 +78406*x^8 +11440*x^9 +8008*x^10 +4368*x^11 +1820*x^12 +560*x^13 +120*x^14 +16*x^15 +x^16) / (1 -x)^16 + O(x^40)) \\ _Colin Barker_, Dec 23 2015

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, J. Serra-Sagrista (jserra(AT)ccd.uab.es)