A048510 - OEIS

%I #20 Sep 08 2022 08:44:57

%S 1,37,122,320,776,1816,4168,9448,21224,47336,104936,231400,507880,

%T 1109992,2416616,5242856,11337704,24444904,52559848,112721896,

%U 241172456,514850792,1096810472,2332033000,4949278696,10485759976,22179479528,46841987048,98784247784

%N a(n) = T(5,n), array T given by A048505.

%C n-th difference of a(n), a(n-1), ..., a(0) is (36, 49, 64, 81, ...).

%H Vincenzo Librandi, <a href="/A048510/b048510.txt">Table of n, a(n) for n = 0..2000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-18,20,-8).

%F a(n) = (n^2+21*n+100) * 2^(n-2) - 24. - _Ralf Stephan_, Feb 05 2004

%F a(n) = 7*a(n-1)-18*a(n-2)+20*a(n-3)-8*a(n-4). - _Colin Barker_, Mar 04 2015

%F G.f.: (112*x^3-119*x^2+30*x+1) / ((x-1)*(2*x-1)^3). - _Colin Barker_, Mar 04 2015

%t LinearRecurrence[{7,-18,20,-8},{1,37,122,320},30] (* _Harvey P. Dale_, Sep 24 2016 *)

%o (Magma) [(n^2+21*n+100) * 2^(n-2) - 24: n in [0..30]]; // _Vincenzo Librandi_, Sep 26 2011

%o (PARI) Vec((112*x^3-119*x^2+30*x+1)/((x-1)*(2*x-1)^3) + O(x^100)) \\ _Colin Barker_, Mar 04 2015

%K nonn,easy

%O 0,2

%A _Clark Kimberling_