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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 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.)