A229147 a(n) = n^4*(3*n+2).

0, 5, 128, 891, 3584, 10625, 25920, 55223, 106496, 190269, 320000, 512435, 787968, 1171001, 1690304, 2379375, 3276800, 4426613, 5878656, 7688939, 9920000, 12641265, 15929408, 19868711, 24551424, 30078125, 36558080, 44109603, 52860416, 62948009, 74520000

Offset: 0

Author

Alois P. Heinz, Sep 15 2013

Keywords

• nonn
• easy

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).

Crossrefs

Row n=5 of A229079.

Cf. A000583, A016789.

Programs

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 *)

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