A229146 a(n) = n^3*(5*n+3)/2.

0, 4, 52, 243, 736, 1750, 3564, 6517, 11008, 17496, 26500, 38599, 54432, 74698, 100156, 131625, 169984, 216172, 271188, 336091, 412000, 500094, 601612, 717853, 850176, 1000000, 1168804, 1358127, 1569568, 1804786, 2065500, 2353489, 2670592, 3018708, 3399796

Offset: 0

Author

Alois P. Heinz, Sep 15 2013

Keywords

• nonn
• easy

Comments

Number of ascending runs in {1,...,n}^4.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

Crossrefs

Row n=4 of A229079.

Programs

Maple

a:= n-> n^3*(5*n+3)/2:
seq(a(n), n=0..40);

Mathematica

Table[n^3(5n+3)/2,{n,0,40}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{0,4,52,243,736},40] (* Harvey P. Dale, Apr 29 2022 *)

Formula

G.f.: -(x^3+23*x^2+32*x+4)*x/(x-1)^5.