A380292 Lagged Fibonacci Generator: a(n) = (100003 - 200003*n + 300007*n^3) mod 10^6 for n <= 55, a(n) = (a(n-24) + a(n-55)) mod 10^6.

200007, 100053, 600183, 500439, 600863, 701497, 602383, 103563, 5079, 106973, 209287, 112063, 615343, 519169, 623583, 728627, 634343, 140773, 47959, 155943, 264767, 174473, 685103, 596699, 709303, 822957, 737703, 253583, 170639, 288913, 408447

Offset

1,1

Comments

Project Euler problem 186 calls this sequence the "Lagged Fibonacci Generator".

Sequence is of period 6615344776548816157229109892561942561580100000. - Jianing Song, Jan 21 2025

Links

Do Thanh Nhan, Table of n, a(n) for n = 1..10000

Project Euler, Problem 186. Connectedness of a Network, with a(n) = S_n.

Kevin Ryde, PARI/GP Code

Jianing Song, Finding the period of A380292

Index entries for linear recurrences with constant coefficients, order 6615344776548816157229109892561942561580100000.

Example

a(5) = 100003 - 200003*5 + 300007*5^3 mod 10^6 = 600863.
a(56) = a(32) + a(1) mod 10^6 = 529290.

Mathematica

A380292[n_] := A380292[n] = Mod[If[n <= 55, 300007*n^3 - 200003*n + 100003, A380292[n-24] + A380292[n-55]], 10^6];
Array[A380292, 50] (* Paolo Xausa, May 20 2025 *)

Prog

(Python)
f = [(100003 - 200003*k + 300007*pow(k, 3, 10**6)) % 10**6 for k in range(1, 56)]
def lagged_fib_gen(n):
  if n < len(f): return f[n-1]
  for i in range(len(f), n+1):
    f.append((f[i-24] + f[i-55]) % 10**6)
  return f[n-1]
(PARI) \\ See links.

Crossrefs

Sequence in context: A106777 A094800 A200863 * A345637 A346350 A345661

Adjacent sequences: A380289 A380290 A380291 * A380293 A380294 A380295

Keyword

nonn,easy

Author

Do Thanh Nhan, Jan 19 2025

Status

approved