A064837 - OEIS

%I #28 Dec 29 2024 18:23:29

%S 0,2,18,114,420,1170,2710,5538,10312,17890,29338,45970,69356,101362,

%T 144158,200258,272528,364226,479010,620978,794676,1005138,1257894,

%U 1559010,1915096,2333346,2821546,3388114,4042108,4793266,5652014,6629506,7737632,8989058,10397234

%N a(n) = (6*n^4 + 30*n^3 - 20*n^2 + 14)*n/30 + (n mod 2).

%H Harry J. Smith, <a href="/A064837/b064837.txt">Table of n, a(n) for n = 0..500</a>

%H G. L. Cohen and E. Tonkes, <a href="https://doi.org/10.37236/1603">Dartboard arrangements</a>, Elect. J. Combin., 8 (No. 2, 2001), #R4.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,5,5,-9,5,-1).

%F From _R. J. Mathar_, Dec 05 2008: (Start)

%F a(n) = 2*A064838(n).

%F G.f.: 2x*(1-x^5-2x^4+x^3+21x^2+4x)/((1-x)^6*(1+x)). (End)

%F a(n) = 5*a(n-1) - 9*a(n-2) + 5*a(n-3) + 5*a(n-4) - 9*a(n-5) + 5*a(n-6) - a(n-7). - _Harvey P. Dale_, Sep 15 2014

%t Table[(6n^4+30n^3-20n^2+14) n/30+Mod[n,2],{n,0,30}] (* or *) LinearRecurrence[ {5,-9,5,5,-9,5,-1},{0,2,18,114,420,1170,2710},40] (* _Harvey P. Dale_, Sep 15 2014 *)

%o (PARI) a(n) = { (6*n^4 + 30*n^3 - 20*n^2 + 14)*n/30 + n%2 } \\ _Harry J. Smith_, Sep 28 2009

%Y Cf. A064838.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Oct 25 2001

%E Better description from _Frank Ellermann_, Mar 16 2002