A317403 a(n)=(-1)^((n-2)*(n-1)/2)*2^(n-1)*n^(n-3).

1, 1, -4, -32, 400, 6912, -153664, -4194304, 136048896, 5120000000, -219503494144, -10567230160896, 564668382613504, 33174037869887488, -2125764000000000000, -147573952589676412928, 11034809241396899282944, 884295678882933431599104, -75613185918270483380568064

Offset

1,3

Comments

Discriminant of Fibonacci polynomials.

Fibonacci polynomials are defined as F(0)=0, F(1)=1 and F(n)=x*F(n-1)+F(n-2) for n>1. Coefficients are given in triangle A168561 with offset 1.

Links

Table of n, a(n) for n=1..19.

Rigoberto Flórez, Robinson Higuita, and Alexander Ramírez, The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials, arXiv:1808.01264 [math.NT], 2018.

Rigoberto Flórez, Robinson Higuita, and Antara Mukherjee, Star of David and other patterns in the Hosoya-like polynomials triangles, 2018.

R. Flórez, R. Higuita and A. Mukherjees, Characterization of the strong divisibility property for generalized Fibonacci polynomials, Integers, 18 (2018), Paper No. A14.

R. Flórez, N. McAnally, and A. Mukherjees, Identities for the generalized Fibonacci polynomial, Integers, 18B (2018), Paper No. A2.

Eric Weisstein's World of Mathematics, Discriminant

Eric Weisstein's World of Mathematics, Fibonacci Polynomial

Mathematica

Array[(-1)^((#-2)*(#-1)/2)*2^(#-1)*#^(#-3)&, 20]

Prog

(PARI) concat([1], [poldisc(p) | p<-Vec(x/(1-x^2-y*x) - x + O(x^20))]) \\ Andrew Howroyd, Aug 26 2018
(Magma) [(-1)^((n-2)*(n-1) div 2)*2^(n-1)*n^(n-3): n in [1..20]]; // Vincenzo Librandi, Aug 27 2018

Crossrefs

Cf. A006645, A001629, A001871, A006645, A007701, A045618, A045925, A093967, A168561, A193678, A317404, A317405, A317408, A317451, A318184, A318197.

Essentially the same as A127670.

Sequence in context: A367376 A195762 A127670 * A243468 A317677 A365603

Adjacent sequences: A317400 A317401 A317402 * A317404 A317405 A317406

Keyword

sign

Author

Rigoberto Florez, Aug 26 2018

Status

approved