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A014421 Odd elements in Pascal's triangle.

%I A014421 #19 Jan 05 2025 19:51:34
%S A014421 1,1,1,1,1,1,3,3,1,1,1,1,5,5,1,1,15,15,1,1,7,21,35,35,21,7,1,1,1,1,9,
%T A014421 9,1,1,45,45,1,1,11,55,165,165,55,11,1,1,495,495,1,1,13,715,1287,1287,
%U A014421 715,13,1,1,91,1001,3003,3003,1001,91,1,1,15,105,455,1365,3003,5005
%N A014421 Odd elements in Pascal's triangle.
%C A014421 The number of terms of the n-row is A001316(n). - _Michel Marcus_, Jan 11 2016
%H A014421 Robert Israel, <a href="/A014421/b014421.txt">Table of n, a(n) for n = 0..10070</a> (rows 0 to 375, flattened)
%H A014421 Arvind Ayyer, Amritanshu Prasad, Steven Spallone, <a href="http://arxiv.org/abs/1601.01776">Odd partitions in Young's lattice</a>, arXiv:1601.01776 [math.CO], 2016. See Fig. 3.
%H A014421 A. M. Reiter, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/31-2/reiter.pdf">Determining the dimension of fractals generated by Pascal’s triangle</a>, Fibonacci Quart, 31(2):112-120, 1993.
%e A014421 Triangle starts:
%e A014421 1;
%e A014421 1, 1;
%e A014421 1, 1;
%e A014421 1, 3, 3, 1;
%e A014421 1, 1;
%e A014421 1, 5, 5, 1;
%e A014421 1, 15, 15, 1;
%e A014421 1, 7, 21, 35, 35, 21, 7, 1;
%e A014421 ...
%p A014421 select(type, [seq(seq(binomial(n,k),k=0..n),n=0..20)],odd); # _Robert Israel_, Jan 11 2016
%t A014421 Select[ Flatten[ Table[ Binomial[ n, i ], {n, 0, 20}, {i, 0, n} ] ], OddQ ]
%o A014421 (PARI) tabf(nn) = {for (n=0, nn, for (k=0, n, b = binomial(n, k); if (b % 2, print1(b, ", "))); print(););} \\ _Michel Marcus_, Jan 11 2016
%Y A014421 Cf. A001316, A007318, A014414.
%Y A014421 Cf. A143333. [From _Reinhard Zumkeller_, Oct 24 2010]
%K A014421 nonn,easy,tabf
%O A014421 0,7
%A A014421 _Mohammad K. Azarian_
%E A014421 More terms from _Erich Friedman_
%E A014421 Keyword tabl replaced by tabf by _Reinhard Zumkeller_, Oct 21 2010
%E A014421 Offset changed to 0 by _Michel Marcus_, Jan 11 2016