OFFSET
1,3
COMMENTS
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).
LINKS
Manfred Scheucher, Table of n, a(n) for n = 1..1323
N. Fernandez, Spiro-Fibonacci numbers
Manfred Scheucher, Sage Script
FORMULA
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
EXAMPLE
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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
a(15)-a(38) from Nathaniel Johnston, Apr 26 2011
STATUS
approved