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A014631 Numbers in order in which they appear in Pascal's triangle.

%I A014631 #36 Oct 17 2023 15:12:27
%S A014631 1,2,3,4,6,5,10,15,20,7,21,35,8,28,56,70,9,36,84,126,45,120,210,252,
%T A014631 11,55,165,330,462,12,66,220,495,792,924,13,78,286,715,1287,1716,14,
%U A014631 91,364,1001,2002,3003,3432,105,455,1365,5005,6435,16,560,1820,4368,8008,11440
%N A014631 Numbers in order in which they appear in Pascal's triangle.
%C A014631 A permutation of the natural numbers. - _Robert G. Wilson v_, Jun 12 2014
%C A014631 In Pascal's triangle a(n) occurs the first time in row A265912(n). - _Reinhard Zumkeller_, Dec 18 2015
%H A014631 Reinhard Zumkeller, <a href="/A014631/b014631.txt">Table of n, a(n) for n = 1..10000</a>
%H A014631 Dana G. Korssjoen, Biyao Li, Stefan Steinerberger, Raghavendra Tripathi, and Ruimin Zhang, <a href="https://arxiv.org/abs/2012.04625">Finding structure in sequences of real numbers via graph theory: a problem list</a>, arXiv:2012.04625 [math.CO], 2020-2021.
%H A014631 F. Richman, <a href="https://web.archive.org/web/20160909161208/http://math.fau.edu/Richman/mla/combs.htm">Combinations and Permutations</a>
%H A014631 <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>
%H A014631 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%t A014631 lst = {1}; t = Flatten[Table[Binomial[n, m], {n, 16}, {m, Floor[n/2]}]]; Do[ If[ !MemberQ[lst, t[[n]]], AppendTo[lst, t[[n]] ]], {n, Length@t}]; lst (* _Robert G. Wilson v_ *)
%t A014631 DeleteDuplicates[Flatten[Table[Binomial[n,m],{n,20},{m,0,Floor[n/2]}]]] (* _Harvey P. Dale_, Apr 08 2013 *)
%o A014631 (Haskell)
%o A014631 import Data.List (nub)
%o A014631 a014631 n = a014631_list !! (n-1)
%o A014631 a014631_list = 1 : (nub $ concatMap tail a034868_tabf)
%o A014631 -- _Reinhard Zumkeller_, Dec 19 2015
%o A014631 (Python)
%o A014631 from itertools import count, islice
%o A014631 def A014631_gen(): # generator of terms
%o A014631     s, c =(1,), set()
%o A014631     for i in count(0):
%o A014631         for d in s:
%o A014631             if d not in c:
%o A014631                 yield d
%o A014631                 c.add(d)
%o A014631         s=(1,)+tuple(s[j]+s[j+1] for j in range(len(s)-1)) + ((s[-1]<<1,) if i&1 else ())
%o A014631 A014631_list = list(islice(A014631_gen(),30)) # _Chai Wah Wu_, Oct 17 2023
%Y A014631 Cf. A034356, A074909, A119629.
%Y A014631 Cf. A034868, A119629 (inverse), A265912.
%K A014631 nonn,easy
%O A014631 1,2
%A A014631 _Mohammad K. Azarian_
%E A014631 More terms from _Erich Friedman_
%E A014631 Offset changed by _Reinhard Zumkeller_, Dec 18 2015