A113770 - OEIS

%I #20 Sep 08 2022 08:45:23

%S 1,10,26,42,58,74,90,106,122,138,154,170,186,202,218,234,250,266,282,

%T 298,314,330,346,362,378,394,410,426,442,458,474,490,506,522,538,554,

%U 570,586,602,618,634,650,666,682,698,714,730,746,762,778,794

%N Partial sums of A113311(n)^2.

%C Central coefficients of number triangle A115284.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F G.f.: (1+8*x+7*x^2)/(1-x)^2.

%F a(n) = 7*0^n + 2*(8*n-3).

%F a(n) = sum{k=0..n, (4-C(1, k)-2*C(0, k))^2}.

%F a(n) = A115284(2n, n).

%F a(0)=1, a(1)=10, a(2)=26, a(n) = 2*a(n-1)-a(n-2). [_Harvey P. Dale_, Aug 19 2011]

%t Accumulate[CoefficientList[Series[(1+x)^2/(1-x),{x,0,110}],x]^2] (* or *) Join[{1},LinearRecurrence[{2,-1},{10,26},110]] (* _Harvey P. Dale_, Aug 19 2011 *)

%o (PARI) Vec((1+8*x+7*x^2)/(1-x)^2 + O(x^80)) \\ _Michel Marcus_, Feb 12 2016

%o (Magma) I:=[1,10,26]; [n le 3 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..60]]; // _Vincenzo Librandi_, Feb 12 2016

%K easy,nonn

%O 0,2

%A _Paul Barry_, Jan 19 2006