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A094925 A hexagonal spiral Fibonacci sequence. 2

%I

%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 ......a(6)..a(7)..a(8)

%C ...a(5)..a(1)..a(2)..a(9)

%C a(14).a(4)..a(3)..a(10)

%C ...a(13).a(12).a(11)

%C Then a(1)=1, a(n)=a(n-1)+Sum{a(i) : a(i) adjacent to a(n-1)}. 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

%e thus:

%e ......12....20...34

%e ...7.....1.....1.....55

%e 638...4.....2.....90

%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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Last modified May 26 05:23 EDT 2019. Contains 323579 sequences. (Running on oeis4.)