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%I #60 Jul 08 2022 13:19:35
%S 1,2,2,3,6,10,15,24,40,65,104,168,273,442,714,1155,1870,3026,4895,
%T 7920,12816,20737,33552,54288,87841,142130,229970,372099,602070,
%U 974170,1576239,2550408,4126648,6677057,10803704,17480760,28284465,45765226
%N a(n) = a(n-1) + a(n-3) + a(n-4), starting with a(0..3) = 1, 2, 2, 3.
%C Shares some properties with Fibonacci sequence.
%C The sum of any two alternating terms (terms separated by one other term) produces a Fibonacci number (e.g., 2+6=8, 3+10=13, 24+65=89). The product of any two consecutive or alternating Fibonacci terms produces a term from this sequence (e.g., 5*8 = 40, 13*5 = 65, 21*8 = 168).
%C In Penney's game (see A171861), the number of ways that HTH beats HHH on flip 3,4,5,... - _Ed Pegg Jr_, Dec 02 2010
%C The Ca2 sums (see A180662 for the definition of these sums) of triangle A035607 equal the terms of this sequence. - _Johannes W. Meijer_, Aug 05 2011
%H Reinhard Zumkeller, <a href="/A070550/b070550.txt">Table of n, a(n) for n = 0..1000</a>
%H David Applegate, Marc LeBrun and N. J. A. Sloane, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Sloane/carry2.html">Dismal Arithmetic</a>, J. Int. Seq., Vol. 14 (2011), Article # 11.9.8.
%H Andreas M. Hinz and Paul K. Stockmeyer, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL25/Hinz/hinz5.html">Precious Metal Sequences and Sierpinski-Type Graphs</a>, J. Integer Seq., Vol 25 (2022), Article 22.4.8.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,1).
%F a(n) = F(floor(n/2)+1)*F(ceiling(n/2)+2), with F(n) = A000045(n). - _Ralf Stephan_, Apr 14 2004
%F G.f.: (1+x)/(1-x-x^3-x^4) = (1+x)/((1+x^2)*(1-x-x^2))
%F a(n) = A126116(n+4) - F(n+3). - _Johannes W. Meijer_, Aug 05 2011
%F a(n) = (1+3*i)/10*(-i)^n + (1-3*i)/10*(i)^n + (2+sqrt(5))/5*((1+sqrt(5))/2)^n + (2-sqrt(5))/5*((1-sqrt(5))/2)^n, where i = sqrt(-1). - _Sergei N. Gladkovskii_, Jul 16 2013
%F a(n+1)*a(n+3) = a(n)*a(n+2) + a(n+1)*a(n+2) for all n in Z. - _Michael Somos_, Jan 19 2014
%F Sum_{n>=1} 1/a(n) = A290565. - _Amiram Eldar_, Feb 17 2021
%e G.f.: 1 + 2*x + 2*x^2 + 3*x^3 + 6*x^4 + 10*x^5 + 15*x^6 + 24*x^7 + ...
%p with(combinat): A070550 := proc(n): fibonacci(floor(n/2)+1) * fibonacci(ceil(n/2)+2) end: seq(A070550(n),n=0..37); # _Johannes W. Meijer_, Aug 05 2011
%t LinearRecurrence[{1, 0, 1, 1}, {1, 2, 2, 3}, 40] (* _Jean-François Alcover_, Jan 27 2018 *)
%o (Haskell)
%o a070550 n = a070550_list !! n
%o a070550_list = 1 : 2 : 2 : 3 :
%o zipWith (+) a070550_list
%o (zipWith (+) (tail a070550_list) (drop 3 a070550_list))
%o -- _Reinhard Zumkeller_, Aug 06 2011
%o (PARI) A070550(n) = fibonacci(n\2+1)*fibonacci((n+5)\2) \\ _M. F. Hasler_, Aug 06 2011
%o (PARI) x='x+O('x^100); Vec((1+x)/(1-x-x^3-x^4)) \\ _Altug Alkan_, Dec 24 2015
%Y Bisections: A001654, A059929.
%Y Cf. A049853, A290565.
%K easy,nonn
%O 0,2
%A Sreyas Srinivasan (sreyas_srinivasan(AT)hotmail.com), May 02 2002
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