A115271 - OEIS

%I #19 Jul 31 2015 18:14:22

%S 1,2,3,4,8,12,16,20,29,38,47,56,72,88,104,120,145,170,195,220,256,292,

%T 328,364,413,462,511,560,624,688,752,816,897,978,1059,1140,1240,1340,

%U 1440,1540,1661,1782,1903,2024,2168,2312,2456,2600,2769,2938

%N Partial sums of floor((n+4)/4)^2.

%C Central coefficients of number triangle A115268.

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1, 0, 2, -4, 2, 0, -1, 2, -1).

%F G.f.: (1+x^4)/((1-x)^2*(1-x^4)^2).

%F a(n) = sum{k=0..n, floor((k+4)/2)^2}.

%F a(n) = A115268(2n, n).

%F a(n) = 2*a(n-1)-a(n-2)+2*a(n-4)-4*a(n-5)+ 2*a(n-6)- a(n-8)+2*a(n-9)-a(n-10) with a(0)=1, a(1)=2, a(2)=3, a(3)=4, a(4)=8, a(5)=12, a(6)=16, a(7)=20, a(8)=29, a(9)=38. - _Harvey P. Dale_, Jun 07 2011

%F a(n) = (2*n^3+18*n^2+61*n+75+3*(n+3)*(-1)^n+6*(n+4-(n+2)*(-1)^n)*(-1)^((2*n-1+(-1)^n)/4))/96. - _Luce ETIENNE_, Mar 17 2015

%t Accumulate[Table[Floor[(n+4)/4]^2,{n,0,50}]] (* or *) LinearRecurrence[ {2,-1,0,2,-4,2,0,-1,2,-1},{1,2,3,4,8,12,16,20,29,38},50] (* _Harvey P. Dale_, Jun 07 2011 *)

%K easy,nonn

%O 0,2

%A _Paul Barry_, Jan 18 2006