cp's OEIS Frontend

A370754 a(n) = 2 + n^2*floor((n+3)/2) + floor(3*n/2).

%I A370754 #22 Mar 09 2024 10:32:15
%S A370754 5,13,33,56,109,155,257,334,501,617,865,1028,1373,1591,2049,2330,2917,
%T A370754 3269,4001,4432,5325,5843,6913,7526,8789,9505,10977,11804,13501,14447,
%U A370754 16385,17458,19653,20861,23329,24680,27437,28939,32001,33662,37045,38873,42593,44596
%N A370754 a(n) = 2 + n^2*floor((n+3)/2) + floor(3*n/2).
%C A370754 {1, 2, n+2, n^2+n+2, a(n)} is the lexicographically first set of 5 positive integers with the property that the sum of any n nondecreasing terms (repetitions allowed) is unique.
%H A370754 Paolo Xausa, <a href="/A370754/b370754.txt">Table of n, a(n) for n = 1..10000</a>
%H A370754 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 A370754 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 A370754 Kevin O'Bryant, <a href="https://arxiv.org/abs/2312.10910">B_h-sets and Rigidity</a>, arXiv:2312.10910 [math.NT], 2023.
%H A370754 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3,-3,3,1,-1).
%F A370754 Column 5 of A347570.
%F A370754 a(n) = A369817(n) + 1.
%F A370754 a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4) + 3*a(n-5) + a(n-6) - a(n-7) for n > 7.
%F A370754 G.f.: x*(-2*x^6 + x^5 + 8*x^4 - x^3 + 5*x^2 + 8*x + 5)/((x - 1)*(x^2 - 1)^3).
%t A370754 A370754[n_] := 2 + n^2*Floor[(n+3)/2] + Floor[3*n/2]; Array[A370754, 50] (* or *)
%t A370754 LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {5, 13, 33, 56, 109, 155, 257}, 50] (* _Paolo Xausa_, Mar 08 2024 *)
%Y A370754 Cf. A347570, A365515, A369817.
%K A370754 nonn,easy
%O A370754 1,1
%A A370754 _Chai Wah Wu_, Feb 29 2024