OFFSET
0,3
COMMENTS
The name of this sequence is derived from its main purpose as a formula for A100982 (see link). Both formulas below stem from Mike Winkler's 2017 paper on the 3x+1 problem (see below), in which a recursive definition of A100982 and A076227 is created in 2-D space. These formulas redefine the sequences in terms of this 1-D recursive sequence.
LINKS
Mike Winkler, The algorithmic structure of the finite stopping time behavior of the 3x + 1 function, arXiv:1709.03385 [math.GM], 2017.
FORMULA
PROG
(Python)
import math
numberOfTerms = 20
L6 = [1, 0]
def c(n):
return math.floor(n/(math.log2(3)-1))
def p(a, b):
return math.factorial(a)/(math.factorial(a-b)*math.factorial(b))
def anotherTerm(newTermCount):
global L6
for a in range(newTermCount+1-len(L6)):
y = len(L6)
newElement = 0
for k in range(y):
newElement -= int(L6[k]*p(c(y)+y-k-2, c(y)-2))
L6.append(newElement)
anotherTerm(numberOfTerms)
print("A325904")
for a in range(numberOfTerms+1):
print(a, "|", L6[a])
(SageMath)
@cached_function
def a(n):
if n < 2: return 0^n
A = floor(n/(log(3, 2) - 1)) - 2
return -sum(a(k)*binomial(A + n - k, A) for k in (0..n-1))
[a(n) for n in range(100)] # Peter Luschny, Sep 10 2019
CROSSREFS
KEYWORD
sign
AUTHOR
Benjamin Lombardo, Sep 08 2019
STATUS
approved