A158498 a(n) = (1/2)*(n^3 - 6*n^2 + 13*n - 6).

1, 2, 3, 7, 17, 36, 67, 113, 177, 262, 371, 507, 673, 872, 1107, 1381, 1697, 2058, 2467, 2927, 3441, 4012, 4643, 5337, 6097, 6926, 7827, 8803, 9857, 10992, 12211, 13517, 14913, 16402, 17987, 19671, 21457, 23348, 25347, 27457, 29681

Offset: 1

Author

Alexander R. Povolotsky, Jan 13 2011

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A000027, A000578.

Programs

Magma

A158498:= func< n | ((n-2)^3+n+2)/2 >;
[A158498(n): n in [1..50]]; // G. C. Greubel, Mar 18 2025

Mathematica

Table[((n-2)^3+n+2)/2, {n,50}] (* or *) LinearRecurrence[{4,-6,4,-1}, {1,2,3,7}, 50] (* G. C. Greubel, Feb 19 2017; Mar 18 2025 *)

PARI

my(x='x+O('x^50)); Vec(x*(1 - 2*x + x^2 + 3*x^3) / (1-x)^4) \\ G. C. Greubel, Feb 19 2017

PARI

a(n)=(n^3 - 6*n^2 + 13*n - 6)/2 \\ Charles R Greathouse IV, Feb 19 2017

SageMath

def A158498(n): return ((n-2)^3 +n+2)//2
print([A158498(n) for n in range(1,51)]) # G. C. Greubel, Mar 18 2025

Formula

a(n) = (1/2)*(n^3 - 6*n^2 + 13*n - 6).

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

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - G. C. Greubel, Feb 19 2017

From G. C. Greubel, Mar 18 2025: (Start)

a(n) = (1/2)*(A000578(n-2) + A000027(n+2)).

E.g.f.: 3 - (1/2)*(6 - 8*x + 3*x^2 - x^3)*exp(x). (End)