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.
Northwest corner: 1 4 9 16 25 37 51 67 2 6 12 20 30 43 58 76 3 8 15 24 35 49 65 83 5 11 19 29 41 56 73 92 7 14 23 34 47 63 81 101 10 18 28 40 54 71 90 111
r = Sqrt[5]; z = 100;
s[0] = 1; s[n_] := s[n] = s[n - 1] + 1 + Floor[n*r];
u = Table[n + 1 + Sum[Floor[(n - k)/r], {k, 0, n}], {n, 0, z}] (* A022780 , col 1 of A283941 *)
v = Table[s[n], {n, 0, z}] (* A022779, row 1 of A283941*)
w[i_, j_] := u[[i]] + v[[j]] + (i - 1)*(j - 1) - 1;
Grid[Table[w[i, j], {i, 1, 10}, {j, 1, 10}]] (* A283941, array *)
Flatten[Table[w[k, n - k + 1], {n, 1, 20}, {k, 1, n}]] (* A283941, sequence *)
r = sqrt(5);
z = 100;
s(n) = if(n<1, 1, s(n - 1) + 1 + floor(n*r));
p(n) = n + 1 + sum(k=0, n, floor((n - k)/r));
u = v = vector(z + 1);
for(n=1, 101, (v[n] = s(n - 1)));
for(n=1, 101, (u[n] = p(n - 1)));
w(i, j) = u[i] + v[j] + (i - 1) * (j - 1) - 1;
tabl(nn) = {for(n=1, nn, for(k=1, n, print1(w(k, n - k + 1), ", "); );
print(); ); };
tabl(20) \\ Indranil Ghosh, Mar 21 2017
from sympy import sqrt
import math
def s(n): return 1 if n<1 else s(n - 1) + 1 + int(math.floor(n*sqrt(5)))
def p(n): return n + 1 + sum([int(math.floor((n - k)/sqrt(5))) for k in range(0, n+1)])
v=[s(n) for n in range(0, 101)]
u=[p(n) for n in range(0, 101)]
def w(i,j): return u[i - 1] + v[j - 1] + (i - 1) * (j - 1) - 1
for n in range(1, 11):
print([w(k, n - k + 1) for k in range(1, n + 1)]) # Indranil Ghosh, Mar 21 2017
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