A048507 - OEIS

%I #24 Sep 08 2022 08:44:57

%S 1,10,35,101,269,685,1693,4093,9725,22781,52733,120829,274429,618493,

%T 1384445,3080189,6815741,15007741,32899069,71827453,156237821,

%U 338690045,731906045,1577058301,3388997629,7264534525,15535702013,33151778813,70598524925

%N a(n) = T(2,n), array T given by A048505.

%C n-th difference of a(n), a(n-1), ..., a(0) is (9, 16, 25, 36, 49, ...).

%H Vincenzo Librandi, <a href="/A048507/b048507.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+9*n+16) * 2^(n-2) - 3. - _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_, Nov 27 2014

%F G.f.: (16*x^3-17*x^2+3*x+1) / ((x-1)*(2*x-1)^3). - _Colin Barker_, Nov 27 2014

%t LinearRecurrence[{7,-18,20,-8},{1,10,35,101},30] (* _Harvey P. Dale_, Jan 21 2021 *)

%o (Magma) [(n^2+9*n+16) * 2^(n-2) - 3: n in [0..30]]; // _Vincenzo Librandi_, Sep 26 2011

%o (PARI) Vec((16*x^3-17*x^2+3*x+1)/((x-1)*(2*x-1)^3) + O(x^100)) \\ _Colin Barker_, Nov 27 2014

%K nonn,easy

%O 0,2

%A _Clark Kimberling_