cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A329722 a(n) = Sum_{k=0..n} ((binomial(n+2k,2n-k)*binomial(n,k)) mod 2).

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%I A329722 #18 Sep 28 2021 01:21:39
%S A329722 1,1,1,2,1,1,2,1,1,1,1,2,2,2,1,3,1,1,1,2,1,1,2,1,2,2,2,4,1,1,3,4,1,1,
%T A329722 1,2,1,1,2,1,1,1,1,2,2,2,1,3,2,2,2,4,2,2,4,2,1,1,1,2,3,3,4,7,1,1,1,2,
%U A329722 1,1,2,1,1,1,1,2,2,2,1,3,1,1,1,2,1,1,2,1,2,2,2,4,1,1
%N A329722 a(n) = Sum_{k=0..n} ((binomial(n+2k,2n-k)*binomial(n,k)) mod 2).
%C A329722 Run length transform of the coefficients of (1-2x^3)/(1-x-x^2), i.e., 1, 1, 2, 1, 3, 4, 7, 11, ... (1, 1 followed by the Lucas sequence A000032).
%H A329722 Chai Wah Wu, <a href="/A329722/b329722.txt">Table of n, a(n) for n = 0..10000</a>
%H A329722 Chai Wah Wu, <a href="https://arxiv.org/abs/1610.06166">Sums of products of binomial coefficients mod 2 and run length transforms of sequences</a>, arXiv:1610.06166 [math.CO], 2016.
%o A329722 (PARI) a(n) = sum(k=0, n, lift(Mod((binomial(n+2*k,2*n-k)*binomial(n,k)), 2))) \\ _Felix Fröhlich_, Nov 25 2019
%o A329722 (Python)
%o A329722 def A329722(n): return sum(int(not (~(n+2*k) & 2*n-k) | (~n & k)) for k in range(n+1)) # _Chai Wah Wu_, Sep 28 2021
%Y A329722 Cf. A000032, A329723.
%K A329722 nonn
%O A329722 0,4
%A A329722 _Chai Wah Wu_, Nov 19 2019