%I A075156
%S A075156 5,6,10,24,70,216,664,2008,5998,17808,52770,156360,463492,1374392,
%T A075156 4076222,12090144,35859742,106359928,315460168,935639768,2775057510,
%U A075156 8230670416,24411730298,72403913480,214746249796,636926269816
%N A075156 Binomial transform of pentanacci numbers A074048: a(n)=Sum(Binomial(n,
               k)*A074048(k),(k=0,..,n)).
%H A075156 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%F A075156 a(n)=6a(n-1)-13a(n-2)+14a(n-3)-7a(n-4)+2a(n-5), a(0)=5, a(1)=6, a(2)=10, 
               a(3)=24, a(4)=70. G.f.: (5-24*x+39*x^2-28*x^3+7*x^4)/(1-6*x+13*x^2-14*x^3+7*x^4-2*x^5)
%F A075156 a(n) = term (1,5) in the 1x5 matrix [70,24,10,6,5] . [6,1,0,0,0; -13,
               0,1,0,0; 14,0,0,1,0; -7,0,0,0,1; 2,0,0,0,0]^n. - Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Jul 25 2008
%p A075156 M := Matrix(5, (i,j)-> if (i=j-1) then 1 elif j>1 then 0 else [6,-13,
               14,-7,2][i] fi); a := n -> (Matrix([[70,24,10,6,5]]).M^(n))[1,5]; 
               seq (a(n), n=0..50); - Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Jul 25 2008
%t A075156 CoefficientList[Series[(5-24*x+39*x^2-28*x^3+7*x^4)/(1-6*x+13*x^2-14*x^3+7*x^4-2*x^5), 
               {x, 0, 25}], x]
%Y A075156 Cf. A074048.
%Y A075156 Sequence in context: A056050 A035111 A035282 this_sequence A075904 A018834 
               A029943
%Y A075156 Adjacent sequences: A075153 A075154 A075155 this_sequence A075157 A075158 
               A075159
%K A075156 easy,nonn
%O A075156 0,1
%A A075156 Mario Catalani (mario.catalani(AT)unito.it), Sep 07 2002