A069008 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) = z(n).

1, 4, 18, 74, 309, 1280, 5313, 22035, 91410, 379171, 1572857, 6524375, 27063881, 112264055, 465684247, 1931711700, 8012962189, 33238687760, 137877896315, 571933356551, 2372445281505, 9841175633650, 40822327332150, 169335704473650, 702423959724591

Offset: 0

Author

Benoit Cloitre, Apr 02 2002

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (3,6,-4,-5,1,1).

Crossrefs

Cf. A006359, A069007, A069008, A069009, A070778, A006359 (offset), for x(n), y(n), z(n), t(n), u(n), v(n).

Programs

Maple

a:= n->(Matrix(6, (i, j)->`if`(i+j>7, 0, 1))^n.<<[1$6][]>>)[3, 1]:
seq(a(n), n=0..30);  # Alois P. Heinz, Jun 14 2013

Mathematica

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][[3]]; Table[a[n], {n, 0, 24}] (* Jean-François Alcover, Jun 18 2013 *)

Formula

G.f.: -(x+1) / (x^6+x^5-5*x^4-4*x^3+6*x^2+3*x-1). - Colin Barker, Jun 14 2013

Extensions

Edited by Henry Bottomley, May 06 2002