A318197 a(n) = 2^((n - 1)*(n + 2)/2)*3^(n*(n - 1))*n^n.

1, 144, 629856, 69657034752, 178523361331200000, 10072680467275913619308544, 12094526244510115670028303294529536, 301689370251168256106930569591201258430005248, 153543958878683931150976515367278080485732740052794998784, 1572290138917723454985999517360927544173903258140620787548160000000000

Offset: 1

Author

Rigoberto Florez, Aug 20 2018

Keywords

• nonn

Comments

Discriminant of Fermat-Lucas polynomials.

Fermat-Lucas polynomials are defined as F(0) = 2, F(1) = 3*x and F(n) = 3*x*F(n - 1) - 2*F(n - 2) for n > 1.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..30
• Rigoberto Flórez, Robinson Higuita, and Alexander Ramírez, The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials, arXiv:1808.01264 [math.NT], 2018.
• R. Flórez, R. Higuita, and A. Mukherjee, The Star of David and Other Patterns in Hosoya Polynomial Triangles, Journal of Integer Sequences, Vol. 21 (2018), Article 18.4.6.
• R. Flórez, N. McAnally, and A. Mukherjees, Identities for the generalized Fibonacci polynomial, Integers, 18B (2018), Paper No. A2.
• R. Flórez, R. Higuita and A. Mukherjees, Characterization of the strong divisibility property for generalized Fibonacci polynomials, Integers, 18 (2018), Paper No. A14.
• Eric Weisstein's World of Mathematics, Discriminant
• Eric Weisstein's World of Mathematics, Fermat-Lucas polynomials

Crossrefs

Cf. A137372, A193678, A007701, A007701, A193678.

Programs

Magma

[2^((n - 1)*(n + 2) div 2)*3^(n*(n - 1))*n^n: n in [1..10]]; // Vincenzo Librandi, Aug 25 2018

Mathematica

Array[2^((# - 1) (# + 2)/2)*3^(# (# - 1))*#^# &, 10] (* Michael De Vlieger, Aug 22 2018 *)

PARI

apply(poldisc, Vec((2-3*x*y)/(1-3*y*x+2*x^2) - 2 + O(x^12))) \\ Andrew Howroyd, Aug 20 2018

PARI

a(n) = 2^((n - 1)*(n + 2)/2)*3^(n*(n - 1))*n^n; \\ Andrew Howroyd, Aug 20 2018