A065033 1 appears three times, other numbers twice.

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, 31, 31, 32, 32, 33, 33, 34, 34, 35

Offset

0,4

Comments

Gives the number of terms in n-th 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).

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

Formula

a(0)=a(1)=a(2)=1, a(3)=2, a(n) = a(n-1)+a(n-2)-a(n-3) for n>3 . G.f.: (1-x^2+x^3)/(1-x-x^2+x^3). - Philippe Deléham, Sep 28 2006

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: A127365 A130472 A076938 * A080513 A004526 A140106

Adjacent sequences: A065030 A065031 A065032 * A065034 A065035 A065036

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 04 2001

Status

approved