A038235 Bottom line of 4-wave sequence A038197, also bisection of A006357.

1, 10, 85, 707, 5864, 48620, 403104, 3342081, 27708726, 229729153, 1904652103, 15791202736, 130922641160, 1085461206128, 8999406210929, 74612811302754, 618604325665341, 5128761469382475, 42521840081752984, 352542596245147348

Offset: 0

Author

Floor van Lamoen

Keywords

• nonn
• easy

Links

• F. v. Lamoen, Wave sequences
• Index entries for linear recurrences with constant coefficients, signature (10,-15,7,-1)

Programs

Mathematica

LinearRecurrence[{10,-15,7,-1},{1,10,85,707},20] (* Harvey P. Dale, Nov 24 2019 *)

PARI

k=4; 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(4)=(1, 1, 1, 1), let M(4) be the 4 X 4 matrix m(i, j) = min(i, j); then a(n) = max(v(4)*M(4)^n). - Benoit Cloitre, Oct 03 2002

From Floor van Lamoen, Sep 13 2006: (Start)

a(n) = 10a(n-1) - 15a(n-2) + 7a(n-3) - a(n-4).

G.f.: 1/(1 - 10x + 15x^2 - 7x^3 + x^4). (End)