A048469 - OEIS

%I #20 Aug 07 2024 06:05:34

%S 1,10,29,69,153,329,697,1465,3065,6393,13305,27641,57337,118777,

%T 245753,507897,1048569,2162681,4456441,9175033,18874361,38797305,

%U 79691769,163577849,335544313,687865849,1409286137,2885681145,5905580025,12079595513,24696061945

%N a(n) = T(8,n), array T given by A047858.

%C n-th difference of a(n), a(n-1), ..., a(0) is (9, 10, 11, ...).

%H Vincenzo Librandi, <a href="/A048469/b048469.txt">Table of n, a(n) for n = 0..3000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-8,4).

%F Main diagonal of the array defined by T(0, j) = j+1 for j>=0, T(i, 0) = i+1 for i>=0, T(i, j) = T(i-1, j-1) + T(i-1, j) +  7. - _Benoit Cloitre_, Jun 17 2003

%F a(n) = 2^(n-1)*(n+16)-7. a(0)=1, a(1)=10, a(2)=29, a(n) = 5*a(n-1)-8*a(n-2)+4*a(n-3). - _Vincenzo Librandi_, Sep 28 2011

%F G.f.: (1+5*x-13*x^2) / ((1-x)*(1-2*x)^2). - _Colin Barker_, Feb 18 2016

%t LinearRecurrence[{5,-8,4},{1,10,29},40] (* _Harvey P. Dale_, Aug 15 2020 *)

%o (Magma) [2^(n-1)*(n+16)-7: n in [0..30]]; // _Vincenzo Librandi_, Sep 28 2011

%K nonn,easy

%O 0,2

%A _Clark Kimberling_