A338399 Inverse boustrophedon transform of the Fibonacci numbers.

0, 1, -1, 2, -7, 15, -78, 293, -1629, 8992, -58105, 404669, -3097456, 25617669, -228373197, 2180640110, -22212371403, 240392198791, -2754699284494, 33320193986081, -424246016043385, 5671750867032228, -79436475109286061, 1163129092965592997

Offset

0,4

Links

Table of n, a(n) for n=0..23.

Eric Weisstein's World of Mathematics, Boustrophedon Transform

Wikipedia, Boustrophedon transform

Index entries for sequences related to boustrophedon transform

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A000111(n-k) * A000045(k).

E.g.f.: -(2/sqrt(5)) * exp(x/2) * sinh((sqrt(5)/2)*x) * cos(x) / (1-sin(x)).

Prog

(Python)
import sympy
def A338399(n):
  T=[]
  for k in range(n+1):
    T.append(sympy.fibonacci(k))
    T.reverse()
    for i in range(k):
      T[i+1]=T[i]-T[i+1]
  return T[-1]
(Python)
from itertools import accumulate, islice
from operator import sub
def A338399_gen(): # generator of terms
    blist, a, b = tuple(), 0, 1
    while True:
        yield (blist := tuple(accumulate(reversed(blist), func=sub, initial=a)))[-1]
        a, b = b, a+b
A338399_list = list(islice(A338399_gen(), 20)) # Chai Wah Wu, Jun 10 2022

Crossrefs

Cf. A000045, A000111, A000738.

Sequence in context: A050612 A120110 A047694 * A262016 A129666 A288675

Adjacent sequences: A338396 A338397 A338398 * A338400 A338401 A338402

Keyword

sign

Author

Pontus von Brömssen, Oct 24 2020

Status

approved