OFFSET
0,2
COMMENTS
Number of ascending runs in {1,...,n}^5.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
G.f.: (x^4+58*x^3+198*x^2+98*x+5)*x/(x-1)^6.
a(0)=0, a(1)=5, a(2)=128, a(3)=891, a(4)=3584, a(5)=10625, a(n)= 6*a(n-1)- 15*a(n-2)+ 20*a(n-3)- 15*a(n-4)+ 6*a(n-5)- a(n-6). - Harvey P. Dale, Aug 14 2015
E.g.f.: exp(x)*x*(5 + 59*x + 87*x^2 + 32*x^3 + 3*x^4). - Stefano Spezia, Jul 17 2024
MAPLE
a:= n-> n^4*(3*n+2):
seq(a(n), n=0..40);
MATHEMATICA
Table[n^4 (3n+2), {n, 0, 30}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 5, 128, 891, 3584, 10625}, 40] (* Harvey P. Dale, Aug 14 2015 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Sep 15 2013
STATUS
approved