The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A354336 a(n) is the integer w such that (L(2*n)^2, -L(2*n-1)^2, -w) is a primitive solution to the Diophantine equation 2*x^3 + 2*y^3 + z^3 = 125, where L(n) is the n-th Lucas number (A000032). 2
 1, 11, 61, 401, 2731, 18701, 128161, 878411, 6020701, 41266481, 282844651, 1938646061, 13287677761, 91075098251, 624238009981, 4278590971601, 29325898791211, 201002700566861, 1377693005176801, 9442848335670731, 64722245344518301, 443612869075957361 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Subsequence of A017281. LINKS Table of n, a(n) for n=0..21. Index entries for linear recurrences with constant coefficients, signature (8,-8,1). FORMULA a(n) = (-125 + 2*A005248(n)^6 - 2*A002878(n-1)^6)^(1/3). a(n) = Lucas(4*n+1) - Lucas(4*n-2] + 3 = A056914(n) - 15*A092521(n-1), for n > 1. a(n) = Lucas(4*n+1) + 1 - Lucas(2*n-1)^2. a(n) = 2*A081015(n-1) + 1. a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3). G.f.: (1 + 3*x - 19*x^2)/((1 - x)*(1 - 7*x + x^2)). - Stefano Spezia, Jun 22 2022 EXAMPLE 2*(L(4)^2)^3 + 2*(-L(3)^2)^3 + (-61)^3 = 2*(49)^3 + 2*(-1)^3 + (-61)^3 = 125, a(2) = 61. MATHEMATICA LucasL[4*Range[22]-3] + 1 - LucasL[2*Range[22]-3]^2 CROSSREFS Cf. A000032, A002878, A005248, A017281, A056914, A081015, A092521. Cf. A337928, A354337. Sequence in context: A156095 A068846 A092164 * A088545 A259257 A289646 Adjacent sequences: A354333 A354334 A354335 * A354337 A354338 A354339 KEYWORD nonn,easy AUTHOR XU Pingya, Jun 20 2022 STATUS approved

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

Last modified April 16 14:05 EDT 2024. Contains 371740 sequences. (Running on oeis4.)