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 A094925 A hexagonal spiral Fibonacci sequence. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A094926, A078510, A079421, A079422. Sequence in context: A005182 A329397 A172524 * A289168 A340217 A289000 Adjacent sequences: A094922 A094923 A094924 * A094926 A094927 A094928 KEYWORD nonn,easy AUTHOR EXTENSIONS a(15)-a(38) from Nathaniel Johnston, Apr 26 2011 STATUS approved

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Last modified January 29 23:01 EST 2023. Contains 359939 sequences. (Running on oeis4.)