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 A213387 #52 Jun 23 2025 10:54:40
%S A213387 0,2,9,26,63,140,297,614,1251,2528,5085,10202,20439,40916,81873,
%T A213387 163790,327627,655304,1310661,2621378,5242815,10485692,20971449,
%U A213387 41942966,83886003,167772080,335544237,671088554,1342177191
%N A213387 a(n) = 5*2^(n-1) - 2 - 3*n.
%C A213387 Create an array m(i,j) as follows: m(1,j) = j*(j-1)/2 in the top row, m(i,1) = (i-1)^2 in the left column, and m(i,j) = m(i,j-1) + m(i-1,j) recursively in the main body, j >= 1, i >= 1. The sum of the terms in an antidiagonal is one term in this sequence, a(n) = Sum_{k=1..n} m(n-k+1,k).
%H A213387 Harvey P. Dale, <a href="/A213387/b213387.txt">Table of n, a(n) for n = 1..1000</a>
%H A213387 Joseph Breen and Emma Copeland, <a href="https://arxiv.org/abs/2506.12612">Non-orientable Nurikabe</a>, arXiv:2506.12612 [math.CO], 2025. See pp. 1, 4.
%H A213387 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2).
%F A213387 a(n) = A095151(n-1) + 2*A000295(n-1).
%F A213387 G.f.: x^2*(2+x) / ( (1-2*x)*(1-x)^2 ). - _R. J. Mathar_, Jun 29 2012
%F A213387 a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3); a(1)=0, a(2)=2, a(3)=9. - _Harvey P. Dale_, Sep 28 2012
%e A213387 For n=5, m(5,1)=16, m(4,2)=15, m(3,3)=11, m(2,4)=11, m(1,5)=10 gives the sum 63 = 2*A000295(4) + A095151(4) = 2*11 + 41.
%t A213387 Table[5*2^(n-1)-2-3n,{n,30}] (* or *) LinearRecurrence[{4,-5,2},{0,2,9},30] (* _Harvey P. Dale_, Sep 28 2012 *)
%Y A213387 Cf. A000295, A095151, A000217, A000290.
%K A213387 nonn,easy
%O A213387 1,2
%A A213387 _J. M. Bergot_, Jun 28 2012