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A070550 a(n) = a(n-1) + a(n-3) + a(n-4), starting with a(0..3) = 1, 2, 2, 3. 10
1, 2, 2, 3, 6, 10, 15, 24, 40, 65, 104, 168, 273, 442, 714, 1155, 1870, 3026, 4895, 7920, 12816, 20737, 33552, 54288, 87841, 142130, 229970, 372099, 602070, 974170, 1576239, 2550408, 4126648, 6677057, 10803704, 17480760, 28284465, 45765226 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Shares some properties with Fibonacci sequence.

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 series (e.g., 5*8 = 40, 13*5 = 65, 21*8 = 168).

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

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

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,1,1)

FORMULA

a(n) = F(floor(n/2)+1)*F(ceiling(n/2)+2), with F(n) = A000045(n). - Ralf Stephan, Apr 14 2004

G.f.: (1+x)/(1-x-x^3-x^4) = (1+x)/((1+x^2)*(1-x-x^2))

a(n) = A126116(n+4) - F(n+3). - Johannes W. Meijer, Aug 05 2011

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

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

EXAMPLE

G.f.: 1 + 2*x + 2*x^2 + 3*x^3 + 6*x^4 + 10*x^5 + 15*x^6 + 24*x^7 + ...

MAPLE

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

PROG

(Haskell)

a070550 n = a070550_list !! n

a070550_list = 1 : 2 : 2 : 3 :

   zipWith (+) a070550_list

               (zipWith (+) (tail a070550_list) (drop 3 a070550_list))

-- Reinhard Zumkeller, Aug 06 2011

(PARI) A070550(n) = fibonacci(n\2+1)*fibonacci((n+5)\2) \\ M. F. Hasler, Aug 06 2011

(PARI) x='x+O('x^100); Vec((1+x)/(1-x-x^3-x^4)) \\ Altug Alkan, Dec 24 2015

CROSSREFS

Bisections: A001654, A059929.

Cf. A049853.

Sequence in context: A163493 A054200 A137216 * A185084 A145778 A102762

Adjacent sequences:  A070547 A070548 A070549 * A070551 A070552 A070553

KEYWORD

easy,nonn

AUTHOR

Sreyas Srinivasan (sreyas_srinivasan(AT)hotmail.com), May 02 2002

EXTENSIONS

More terms from Benoit Cloitre, May 03 2002

STATUS

approved

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Last modified May 30 03:15 EDT 2017. Contains 287305 sequences.