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A318197 a(n) = 2^((n - 1)*(n + 2)/2)*3^(n*(n - 1))*n^n. 4
1, 144, 629856, 69657034752, 178523361331200000, 10072680467275913619308544, 12094526244510115670028303294529536, 301689370251168256106930569591201258430005248, 153543958878683931150976515367278080485732740052794998784, 1572290138917723454985999517360927544173903258140620787548160000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

REFERENCES

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.

LINKS

Table of n, a(n) for n=1..10.

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.

Eric Weisstein's World of Mathematics, Discriminant

Eric Weisstein's World of Mathematics, Fermat-Lucas polynomials

MATHEMATICA

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

PROG

(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

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

CROSSREFS

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

Sequence in context: A086778 A227652 A159436 * A193346 A003837 A013863

Adjacent sequences:  A318194 A318195 A318196 * A318198 A318199 A318200

KEYWORD

nonn

AUTHOR

Rigoberto Florez, Aug 20 2018

STATUS

approved

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Last modified January 24 00:58 EST 2019. Contains 319404 sequences. (Running on oeis4.)