cp's OEIS Frontend

A069007 Let M denote the 6 X 6 matrix with rows /1,1,1,1,1,1/1,1,1,1,1,0/1,1,1,1,0,0/1,1,1,0,0,0/1,1,0,0,0,0/1,0,0,0,0,0/ and A(n) the vector (x(n),y(n),z(n),t(n),u(n),v(n)) = M^n*A where A is the vector (1,1,1,1,1,1); then a(n) = y(n).

%I A069007 #20 Mar 26 2024 10:30:57
%S A069007 1,5,20,85,350,1456,6034,25038,103849,430794,1786960,7412548,30748055,
%T A069007 127546530,529077571,2194674687,9103762600,37763453591,156647144355,
%U A069007 649790354877,2695405055655,11180849888139,46379450073255
%N A069007 Let M denote the 6 X 6 matrix with rows /1,1,1,1,1,1/1,1,1,1,1,0/1,1,1,1,0,0/1,1,1,0,0,0/1,1,0,0,0,0/1,0,0,0,0,0/ and A(n) the vector (x(n),y(n),z(n),t(n),u(n),v(n)) = M^n*A where A is the vector (1,1,1,1,1,1); then a(n) = y(n).
%H A069007 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,6,-4,-5,1,1).
%F A069007 G.f.: (x^3+x^2-2*x-1) / (x^6+x^5-5*x^4-4*x^3+6*x^2+3*x-1). [_Colin Barker_, Dec 13 2012]
%p A069007 a:= n->(Matrix(6, (i, j)->`if`(i+j>7, 0, 1))^n.<<[1$6][]>>)[2, 1]:
%p A069007 seq(a(n), n=0..30);  # _Alois P. Heinz_, Jun 18 2013
%t A069007 m = Table[ If[i + j <= 7, 1, 0], {i, 1, 6}, {j, 1, 6}]; mp[n_] := MatrixPower[m, n].m[[1]]; a[n_] := mp[n][[2]]; Table[a[n], {n, 0, 22}] (* _Jean-François Alcover_, Jun 18 2013 *)
%Y A069007 Cf. A006359, A069007, A069008, A069009, A070778, A006359 (offset), for x(n), y(n), z(n), t(n), u(n), v(n).
%K A069007 easy,nonn
%O A069007 0,2
%A A069007 _Benoit Cloitre_, Apr 02 2002
%E A069007 Edited by _Henry Bottomley_, May 06 2002