

A065033


1 appears three times, other numbers twice.


15



1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30
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OFFSET

0,4


COMMENTS

Gives the number of terms in nth row of many common tables.
Number of partitions of the (n+1)th Fibonacci number into distinct Fibonacci numbers: a(n) = A000119(A000045(n)), see also A098641.  Reinhard Zumkeller, Apr 24 2005
a(n) = length of run n+1 of consecutive 4s in A254338.  Reinhard Zumkeller, Feb 27 2015
This is the Engel expansion of A070910 + A096789.  Benedict W. J. Irwin, Dec 16 2016


LINKS

Harry J. Smith, Table of n, a(n) for n = 0..1000
Andrei Asinowski, Cyril Banderier, Valerie Roitner, Generating functions for lattice paths with several forbidden patterns, (2019).


FORMULA

a(0)=a(1)=a(2)= 1, a(3)=2, a(n) = a(n1)+a(n2)a(n3) for n>3 . G.f.: (1x^2+x^3)/(1xx^2+x^3).  Philippe Deléham, Sep 28 2006
a(n) = (3/4)+(1/4)*(1)^(n1)+(1/2)*(n1)+[C(2*n,n) mod 2], with n>=0  Paolo P. Lava, Nov 20 2008
a(n) = floor((n+1)/2) + 0^n.  Reinhard Zumkeller, Feb 27 2015


MATHEMATICA

Array[Floor[#/2] &, 61] /. 0 > 1 (* Michael De Vlieger, Mar 10 2020 *)


PROG

(PARI) { for (n=0, 1000, if (n<3, a=1, if (n%2, a++)); write("b065033.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 03 2009
(Haskell)
a065033 n = 0 ^ n + div (n + 1) 2  Reinhard Zumkeller, Feb 27 2015


CROSSREFS

Cf. A004526, A008619.
Cf. A254338.
Sequence in context: A111660 A244325 A168050 * A001057 A127365 A130472
Adjacent sequences: A065030 A065031 A065032 * A065034 A065035 A065036


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Nov 04 2001


STATUS

approved



