cp's OEIS Frontend

A065033 1 appears three times, other numbers twice.

%I A065033 #49 Aug 05 2025 13:27:11
%S A065033 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,
%T A065033 15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25,25,26,
%U A065033 26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35
%N A065033 1 appears three times, other numbers twice.
%C A065033 Gives the number of terms in n-th row of many common tables.
%C A065033 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
%C A065033 a(n) = length of run n+1 of consecutive 4s in A254338. - _Reinhard Zumkeller_, Feb 27 2015
%C A065033 This is the Engel expansion of A070910 + A096789. - _Benedict W. J. Irwin_, Dec 16 2016
%H A065033 Harry J. Smith, <a href="/A065033/b065033.txt">Table of n, a(n) for n = 0..1000</a>
%H A065033 Andrei Asinowski, Cyril Banderier, and Valerie Roitner, <a href="https://lipn.univ-paris13.fr/~banderier/Papers/several_patterns.pdf">Generating functions for lattice paths with several forbidden patterns</a>, (2019).
%H A065033 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A065033 From _Philippe Deléham_, Sep 28 2006: (Start)
%F A065033 a(n) = a(n-1)+a(n-2)-a(n-3) for n>3.
%F A065033 G.f.: (1-x^2+x^3)/(1-x-x^2+x^3). (End)
%F A065033 a(n) = floor((n+1)/2) + 0^n. - _Reinhard Zumkeller_, Feb 27 2015
%F A065033 E.g.f.: (2 + exp(x)*x + sinh(x))/2. - _Stefano Spezia_, Aug 05 2025
%t A065033 Array[Floor[#/2] &, 61] /. 0 -> 1 (* _Michael De Vlieger_, Mar 10 2020 *)
%o A065033 (PARI) a(n) = { if (n<1, n==0, (n+1)\2) } \\ _Harry J. Smith_, Oct 03 2009
%o A065033 (Haskell)
%o A065033 a065033 n = 0 ^ n + div (n + 1) 2  -- _Reinhard Zumkeller_, Feb 27 2015
%Y A065033 Cf. A004526, A008619.
%Y A065033 Cf. A254338.
%K A065033 nonn,easy
%O A065033 0,4
%A A065033 _N. J. A. Sloane_, Nov 04 2001