A038339 Bottom line of 5-wave sequence A038201, also bisection of A006358.

1, 15, 190, 2353, 29056, 358671, 4427294, 54648506, 674555937, 8326406594, 102777312308, 1268635610806, 15659451261015, 193293024178230, 2385919696236315, 29450689289430149, 363525688224433321

Offset: 0

Author

Floor van Lamoen

Keywords

• nonn

Comments

Denominator of g.f. is sum{k=0..5, (-1)^(k+1)*binomial(10-k,k)x^(5-k)}. This is det(J-x*I) where I is the 5x5 identity matrix and J is the matrix [1 1 0 0 0] [1 2 1 0 0] [0 1 2 1 0] [0 0 1 2 1] [0 0 0 1 2] - Paul Barry, May 11 2006

Links

• F. v. Lamoen, Wave sequences
• Index entries for linear recurrences with constant coefficients, signature (15,-35,28,-9,1).

Programs

PARI

k=5; M(k)=matrix(k,k,i,j,min(i,j)); v(k)=vector(k,i,1); a(n)=vecmax(v(k)*M(k)^n)

Formula

Let v(5)=(1, 1, 1, 1, 1), let M(5) be the 5 X 5 matrix m(i, j) =min(i, j); then a(n)= Max ( v(5)*M(5)^n) - Benoit Cloitre, Oct 03 2002

G.f.: 1/(1-15x+35x^2-28x^3+9x^4-x^5); - Paul Barry, May 11 2006

Extensions

More terms from Benoit Cloitre, Oct 03 2002