A179783 - OEIS

%I #20 Mar 04 2023 15:33:35

%S 1,3,17,39,81,139,225,335,481,659,881,1143,1457,1819,2241,2719,3265,

%T 3875,4561,5319,6161,7083,8097,9199,10401,11699,13105,14615,16241,

%U 17979,19841,21823,23937,26179,28561,31079

%N a(n) = 2*n*(n+1)*(n+2)/3 + (-1)^n.

%C First differences in 2*A081352.

%C Second differences in 4*A004442.

%H B. Berselli, <a href="/A179783/b179783.txt">Table of n, a(n) for n = 0..10000</a>.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).

%F G.f.: (1+10*x^2-4*x^3+x^4)/((1+x)*(1-x)^4); exp(-x)+(2/3)*exp(x)*x*(6+6*x+x^2).

%F a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5) for n>4.

%F a(n) = 4*A000292(n)+(-1)^n.

%t LinearRecurrence[{3,-2,-2,3,-1},{1,3,17,39,81},40] (* _Harvey P. Dale_, Mar 04 2023 *)

%o (Magma) [(2/3)*n*(n+1)*(n+2)+(-1)^n: n in [0..35]];

%o (PARI) for(n=0, 35, print1((2/3)*n*(n+1)*(n+2)+(-1)^n", "));

%Y Cf. A005744, A026035, A175109, A131941.

%K nonn,easy

%O 0,2

%A _Bruno Berselli_, Jul 29 2010 - Sep 07 2010