A240467 Inverse of 152nd cyclotomic polynomial.

1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0

Offset

0

Comments

Periodic with period length 152. - Ray Chandler, Apr 03 2017

In general the expansion of 1/Phi(N) is N-periodic, but also satisfies a linear recurrence of lower order given by degree(Phi(N)) = phi(N) = A000010(N) < N. The signature is given by the coefficients of (1-Phi(N)). - M. F. Hasler, Feb 18 2018

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, order 72, signature (0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1).

Index to sequences related to inverse of cyclotomic polynomials

Mathematica

CoefficientList[Series[1/Cyclotomic[152, x], {x, 0, 200}], x]

Prog

(PARI) Vec(1/polcyclo(152) + O(x^99)) \\ Jinyuan Wang, Feb 28 2020

Crossrefs

Cf. similar sequences (namely 1/Phi(N), N <= 75) listed in A240328.

Cf. also A240465 (76), A014086 (77), A014087 (78), A014093 (84), A014094 (85), A014096 (87), A014099 (90), A014100 (91), A014102 (93), A014104 (95), A014108 (99), A014111 (102), A014114 (105), A014119 (110), A014123 (114), A014124 (115), A014128 (119), A014129 (120), A014135 (126), A014139 (130), A014141 (132), A014142 (133), A014147 (138), A014149 (140), A014152 (143), A014154 (145), A014159 (150), A014163 (154) - A014165 (156), A014170 (161), A014174 (165), A014177 (168), A014179 (170), A014183 (174), A014184 (175), A014189 (180), A014191 (182), A014194 (185) - A014196 (187), A014199 (190), A014204 (195), A014207 (198), A014212 (203), A014218 (209), A014219 (210), A014226 (217), A014229 (220), A014230 (221), A014239 (230), A014240 (231), A014247 (238), A014256 (247), A014262 (253).

Sequence in context: A089510 A138885 A185115 * A014065 A014049 A016371

Adjacent sequences: A240464 A240465 A240466 * A240468 A240469 A240470

Keyword

sign,easy

Author

Vincenzo Librandi, Apr 06 2014

Status

approved