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%I #20 May 04 2021 01:06:59
%S 1,1,2,4,7,12,20,34,55,90,148,240,394,638,1043,1688,2750,4450,7232,
%T 11736,19002,30827,49884,80856,130978,211982,343348,555964,899706,
%U 1456702,2358089,3815834,6176654,9996926,16176330,26180456,42368468,68567892
%N A hexagonal spiral Fibonacci sequence.
%C Consider the following spiral:
%C .
%C a(6)----a(7)----a(8)
%C / \
%C / \
%C / \
%C a(5) a(1)----a(2) a(9)
%C \ / /
%C \ / /
%C \ / /
%C a(14) a(4)----a(3) a(10)
%C \ /
%C \ /
%C \ /
%C a(13)---a(12)---a(11)
%C .
%C 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).
%H Manfred Scheucher, <a href="/A094925/b094925.txt">Table of n, a(n) for n = 1..1323</a>
%H N. Fernandez, <a href="http://www.borve.org/primeness/spirofib.html">Spiro-Fibonacci numbers</a>
%H Manfred Scheucher, <a href="/A094925/a094925.sage.txt">Sage Script</a>
%F 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
%e a(2) = a(1) = 1,
%e a(3) = a(1) + a(2) = 2,
%e a(4) = a(1) + a(2) + a(3) = 4,
%e a(5) = a(1) + a(3) + a(4) = 7,
%e a(6) = a(1) + a(4) + a(5) = 12,
%e a(7) = a(1) + a(5) + a(6) = 20, etc.
%e Thus:
%e 12----20----34
%e / \
%e / \
%e 7 1-----1 55
%e \ / /
%e \ / /
%e 638 4-----2 90
%e \ /
%e \ /
%e 394---240---148
%Y Cf. A094926, A078510, A079421, A079422.
%K nonn,easy
%O 1,3
%A _Yasutoshi Kohmoto_
%E a(15)-a(38) from _Nathaniel Johnston_, Apr 26 2011
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