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.
%I A369817 #35 Mar 09 2024 10:29:18
%S A369817 4,12,32,55,108,154,256,333,500,616,864,1027,1372,1590,2048,2329,2916,
%T A369817 3268,4000,4431,5324,5842,6912,7525,8788,9504,10976,11803,13500,14446,
%U A369817 16384,17457,19652,20860,23328,24679,27436,28938,32000,33661,37044,38872,42592,44595,48668,50854,55296,57673,62500,65076
%N A369817 The fifth term of the greedy B_n set of natural numbers.
%C A369817 {0, 1, n+1, n^2+n+1, a(n)} is the lexicographically first set of 5 nonnegative integers with the property that the sum of any n nondecreasing terms (repetitions allowed) is unique.
%H A369817 M. B. Nathanson, <a href="https://arxiv.org/abs/2310.14426">The third positive element in the greedy B_h-set</a>, arXiv:2310.14426 [math.NT], 2023.
%H A369817 M. B. Nathanson and Kevin O'Bryant, <a href="https://arxiv.org/abs/2311.14021">The fourth positive element in the greedy B_h-set</a>, arXiv:2311.14021 [math.NT], 2023.
%H A369817 Kevin O'Bryant, <a href="https://arxiv.org/abs/2312.10910">B_h-sets and Rigidity</a>, arXiv:2312.10910 [math.NT], 2023.
%H A369817 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3,-3,3,1,-1).
%F A369817 a(n) = floor((n + 3)/2) * n^2 + floor((3*n + 2)/2), proved in arXiv:2311.14021.
%F A369817 G.f.: x*(-x^6 + x^5 + 5*x^4 - x^3 + 8*x^2 + 8*x + 4)/((x - 1)*(x^2 - 1)^3). - _Chai Wah Wu_, Feb 28 2024
%F A369817 E.g.f.: ((2 + 7*x + 5*x^2 + x^3)*cosh(x) + (1 + 6*x + 6*x^2 + x^3)*sinh(x) - 2)/2. - _Stefano Spezia_, Mar 09 2024
%e A369817 a(2) = 12, as all 15 nonincreasing sums from {0,1,3,7,12}, namely 0+0 < 0+1 < 1+1 < 0+3 < 1+3 < 3+3 < 0+7 < 1+7 < 3+7 < 0+12 < 1+12 < 7+7 < 3+12 < 7+12 < 12+12, are distinct, and all other 5-element sets of nonnegative integers with this property are lexicographically after {0,1,3,7,12}.
%t A369817 a[n_] := Floor[(n + 3)/2] n^2 + Floor[(3 n + 2)/2]
%o A369817 (Python)
%o A369817 def A369817(n): return (n+3>>1)*n**2+(3*n+2>>1) # _Chai Wah Wu_, Feb 28 2024
%Y A369817 Column 5 of A365515.
%K A369817 nonn,easy
%O A369817 1,1
%A A369817 _Kevin O'Bryant_, Feb 02 2024