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A325904 Generator sequence for A100982. 2
1, 0, -3, -8, 15, -91, -54, 2531, -17021, 43035, -66258, 1958757, -24572453, 146991979, -287482322, -3148566077, 35506973089, -198639977241, 1006345648929, -8250266425561, 76832268802555, -517564939540551, 1890772860334557, 3323588929061820, -104547561696315008, 907385094824827328, -6313246535826877248 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..26.

Mike Winkler, The algorithmic structure of the finite stopping time behavior of the 3x + 1 function, arXiv:1709.03385 [math.GM], 2017.

FORMULA

a(0)=1, a(1)=0, a(n) = -Sum_{k=0..n-1} a(k)*binomial(A325913(n)+n-k-2, A325913(n)-2) for n>1.

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

Cf. A020914, A076227, A100982.

Sequence in context: A192167 A065500 A120341 * A094357 A136532 A030417

Adjacent sequences:  A325901 A325902 A325903 * A325905 A325906 A325907

KEYWORD

sign

AUTHOR

Benjamin Lombardo, Sep 08 2019

STATUS

approved

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Last modified February 18 15:30 EST 2020. Contains 332019 sequences. (Running on oeis4.)