This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A317451 a(n) = (n*A003500(n) - A231896(n))/2. 5
 0, 2, 16, 92, 464, 2182, 9824, 42936, 183648, 772746, 3209968, 13196564, 53791408, 217700110, 875718080, 3504277360, 13959102912, 55383875346, 218965651152, 862983998924, 3391602170512, 13295446717334, 51999641009696, 202948920530728, 790569797639456, 3074179492922778 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Derivative of Chebyshev second kind polynomials evaluated at 2. 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 Colin Barker, Table of n, a(n) for n = 0..1000 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, 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, Chebyshev Polynomial of the First Kind Index entries for linear recurrences with constant coefficients, signature (8,-18,8,-1). FORMULA From Colin Barker, Aug 06 2018: (Start) G.f.: 2*x / (1 - 4*x + x^2)^2. a(n) = (sqrt(3)*((2-sqrt(3))^n - (2+sqrt(3))^n) + 3*((2-sqrt(3))^(1+n) + (2+sqrt(3))^(1+n))*n) / 18. a(n) = 8*a(n-1) - 18*a(n-2) + 8*a(n-3) - a(n-4) for n>3. (End) MATHEMATICA CoefficientList[ Series[2 x/(x^2 - 4x + 1)^2, {x, 0, 25}], x] (* Robert G. Wilson v, Aug 07 2018 *) PROG (PARI) a(n) = subst(deriv(polchebyshev(n, 2)), x, 2); \\ Michel Marcus, Jul 29 2018. (PARI) concat(0, Vec(2*x / (1 - 4*x + x^2)^2 + O(x^40))) \\ Colin Barker, Aug 06 2018 CROSSREFS Cf. A003500, A231896, A133156 (Chebyshev polynomials of the second kind). Sequence in context: A208008 A208550 A214824 * A220324 A208002 A220932 Adjacent sequences:  A317448 A317449 A317450 * A317452 A317453 A317454 KEYWORD nonn,easy AUTHOR Rigoberto Florez, Jul 28 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 13 17:17 EST 2019. Contains 329970 sequences. (Running on oeis4.)