A094926 -id:A094926 - cp's OEIS frontend

A258639 Decimal expansion of a constant related to A094926.

5, 4, 1, 7, 2, 0, 0, 2, 1, 9, 5, 8, 1, 4, 4, 4, 3, 3, 8, 6, 9, 3, 2, 2, 8, 0, 2, 8, 7, 1, 7, 6, 7, 4, 3, 8, 4, 7, 7, 7, 0, 5, 7, 7, 1, 7, 3, 0, 5, 0, 0, 1, 3, 5, 1, 2, 3, 7, 3, 1, 1, 9, 2, 7, 9, 4, 1, 3, 7, 0, 8, 7, 0, 1, 0, 4, 1, 8, 2, 5, 3, 0, 2, 5, 8, 1, 4, 8, 7, 9, 1, 0, 1, 6, 7, 4, 3, 5, 0, 9, 6, 5, 0, 8, 6, 0

Offset: 0

Manfred Scheucher and Vaclav Kotesovec, Jun 06 2015

			0.541720021958144433869322802871767438477705771730500135123731192794137...

Cf. A094926.

Equals limit n->infinity A094926(n) / phi^n, where phi = A001622 = (1+sqrt(5))/2 is the golden ratio.

A094925 A hexagonal spiral Fibonacci sequence.

Original entry on oeis.org

1, 1, 2, 4, 7, 12, 20, 34, 55, 90, 148, 240, 394, 638, 1043, 1688, 2750, 4450, 7232, 11736, 19002, 30827, 49884, 80856, 130978, 211982, 343348, 555964, 899706, 1456702, 2358089, 3815834, 6176654, 9996926, 16176330, 26180456, 42368468, 68567892

Offset: 1

Yasutoshi Kohmoto

Consider the following spiral:
.
          a(6)----a(7)----a(8)
          /                 \
         /                   \
        /                     \
      a(5)    a(1)----a(2)    a(9)
        \             /       /
         \           /       /
          \         /       /
  a(14)   a(4)----a(3)    a(10)
     \                    /
      \                  /
       \                /
      a(13)---a(12)---a(11)
.
Then a(1)=1, a(n) = a(n-1) + Sum_{a(i) adjacent to a(n-1)} a(i). Here 6 terms around a(m) touch a(m).

			a(2) = a(1) = 1,
a(3) = a(1) + a(2) = 2,
a(4) = a(1) + a(2) + a(3) = 4,
a(5) = a(1) + a(3) + a(4) = 7,
a(6) = a(1) + a(4) + a(5) = 12,
a(7) = a(1) + a(5) + a(6) = 20, etc.
Thus:
         12----20----34
         /             \
        /               \
       7     1-----1    55
        \         /     /
         \       /     /
  638     4-----2    90
     \               /
      \             /
     394---240---148

Manfred Scheucher, Table of n, a(n) for n = 1..1323
N. Fernandez, Spiro-Fibonacci numbers
Manfred Scheucher, Sage Script

Cf. A094926, A078510, A079421, A079422.

a(n) ~ c*phi^n with phi=1.61803... being the golden ratio and c = 0.78529667298898361017570049509486675274402985275383398273772345738007479334754... (conjectured). Cf. A094926. - Manfred Scheucher, Jun 03 2015

a(15)-a(38) from Nathaniel Johnston, Apr 26 2011

cp's OEIS Frontend

A258639 Decimal expansion of a constant related to A094926.

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