A047861 - OEIS

%I #21 Sep 08 2022 08:44:57

%S 1,6,17,41,93,205,445,957,2045,4349,9213,19453,40957,86013,180221,

%T 376829,786429,1638397,3407869,7077885,14680061,30408701,62914557,

%U 130023421,268435453,553648125,1140850685,2348810237,4831838205,9932111869,20401094653,41875931133

%N a(n) = T(4,n), array T given by A047858.

%C n-th difference of a(n), a(n-1), ..., a(0) is (5, 6, 7, ...).

%H Vincenzo Librandi, <a href="/A047861/b047861.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 j>=0, T(i, 0)=i+1 i>=0, T(i, j)=T(i-1, j-1)+T(i-1, j)+ 3; a(n)=2^(n-1)*(n+8)-3. - _Benoit Cloitre_, Jun 17 2003

%F a(0)=1, a(1)=6, a(2)=17, a(n) = 5*a(n-1) -8*a(n-2) +4*a(n-3). - _Vincenzo Librandi_, Sep 28 2011

%F G.f.: (1+x-5*x^2) / ((1-x)*(1-2*x)^2). - _Colin Barker_, Feb 17 2016

%o (Magma) [2^(n-1)*(n+8)-3: n in [0..30]]; // _Vincenzo Librandi_, Sep 28 2011

%o (PARI) Vec((1+x-5*x^2)/((1-x)*(1-2*x)^2) + O(x^40)) \\ _Colin Barker_, Feb 17 2016

%K nonn,easy

%O 0,2

%A _Clark Kimberling_