A033596 a(n) = (n^2 - 1)*(n^2 - 3).

3, 0, 3, 48, 195, 528, 1155, 2208, 3843, 6240, 9603, 14160, 20163, 27888, 37635, 49728, 64515, 82368, 103683, 128880, 158403, 192720, 232323, 277728, 329475, 388128, 454275, 528528, 611523, 703920, 806403, 919680, 1044483, 1181568, 1331715, 1495728, 1674435

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A000290 (n^2), A000583 (n^4), A082109.

Programs

Magma

[(n^2-1)*(n^2-3) : n in [0..30]]; // Wesley Ivan Hurt, Oct 30 2014

Maple

A033596:=n->(n^2-1)*(n^2-3): seq(A033596(n), n=0..30); # Wesley Ivan Hurt, Oct 30 2014

Mathematica

Table[(n^2 - 1)*(n^2 - 3), {n, 0, 30}] (* or *)
CoefficientList[Series[3 (1 - 5 x + 11 x^2 + x^3)/(1 - x)^5, {x, 0, 30}], x] (* Wesley Ivan Hurt, Oct 30 2014 *)
LinearRecurrence[{5,-10,10,-5,1},{3,0,3,48,195},40] (* Harvey P. Dale, Nov 20 2024 *)

PARI

vector(31, n, my(m=n-1); (m^2-1)*(m^2-3)) \\ G. C. Greubel, Mar 05 2020

Sage

[(n^2-1)*(n^2-3) for n in (0..30)] # G. C. Greubel, Mar 05 2020

Formula

From Wesley Ivan Hurt, Oct 30 2014: (Start)

G.f.: 3*(1 -5*x +11*x^2 +x^3)/(1-x)^5.

a(n) = 5*a(n-1) -10*a(n-2) +10*a(n-3) -5*a(n-4) +a(n-5).

a(n) = (n^2-1)*(n^2-3) = (A000290(n)-1)*(A000290(n)-3) = A000583(n) - A082109(n+1). (End)

E.g.f.: (3 - 3*x + 3*x^2 + 6*x^3 + x^4)*exp(x). - G. C. Greubel, Mar 05 2020