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 A289762 #45 Jul 17 2017 04:43:40
%S A289762 1,1,4,2,2,4,9,5,3,3,5,9,16,10,6,4,4,6,10,16,25,17,11,7,5,5,7,11,17,
%T A289762 25,36,26,18,12,8,6,6,8,12,18,26,36,49,37,27,19,13,9,7,7,9,13,19,27,
%U A289762 37,49,64,50,38,28,20,14,10,8,8,10,14,20,28,38,50,64,81,65,51,39,29,21,15,11,9
%N A289762 Triangular array T(m,k) = (m+1-k)^2 + k - 1 with m (row) >= 1 and k (column) >= 1, read by rows.
%C A289762 The n-th row is of length = max(2n, 1) and the row sum is (2n^3 + 6n^2 - 2n) / 3.
%C A289762 Rows m = 2, 3, 5, 11, and 41 (Euler's lucky numbers) give the prime numbers generated by the famous polynomials, but twice each one between m^2.
%H A289762 Miquel Cerda, <a href="/A289762/b289762.txt">Table of n, a(n) for n = 1..306</a>
%H A289762 Miquel Cerda, <a href="/A289762/a289762.pdf">Triangle rows 1..41</a>
%H A289762 Miquel Cerda, <a href="/A289762/a289762_1.pdf">Isosceles triangle Rows 1..41</a>
%F A289762 The formula that gives the integers in the m-th rows can be expressed using quadratic polynomials:
%F A289762 for row m = 1, a(k) = k^2 - 3*k + 3
%F A289762 for row m = 2, a(k) = k^2 - 5*k + 8
%F A289762 for row m = 3, a(k) = k^2 - 7*k + 15
%F A289762 for row m = 4, a(k) = k^2 - 9*k + 24
%F A289762 for row m = 5, a(k) = k^2 - 11*k + 35
%F A289762 for row m = 6, a(k) = k^2 - 13*k + 48
%F A289762 etc.
%e A289762 The m-th row start and end: T(m,1) = m^2, ..., T(m,2m) = m^2.
%e A289762 In general T(m,k) = T(m,2m+1-k).
%e A289762 m\k 1 2 3 4 5 6 7 8 9 10
%e A289762 1 1, 1,
%e A289762 2 4, 2, 2, 4
%e A289762 3 9, 5, 3, 3, 5, 9
%e A289762 4 16, 10, 6, 4, 4, 6, 10, 16
%e A289762 5 25, 17, 11, 7, 5, 5, 7, 11, 17, 25
%e A289762 6 36, 26, 18, 12, 8, 6, 6, 8, 12, 18, ...
%e A289762 7 49, 37, 27, 19, 13, 9, 7, 7, 9, 13, ...
%e A289762 8 64, 50, 38, 28, 20, 14, 10, 8, 8, 10, ...
%e A289762 9 81, 65, 51, 39, 29, 21, 15, 11, 9, 9, ...
%e A289762 10 100, 82, 66, 52, 40, 30 22, 16, 12, 10, ...
%e A289762 The T(m,k) sequence as an isosceles triangle:
%e A289762 1 1
%e A289762 4 2 2 4
%e A289762 9 5 3 3 5 9
%e A289762 16 10 6 4 4 6 10 16
%e A289762 25 17 11 7 5 5 7 11 17 25
%e A289762 36 26 18 12 8 6 6 8 12 18 26 36
%e A289762 49 37 27 19 13 9 7 7 9 13 19 27 37 49
%e A289762 64 50 38 28 20 14 10 8 8 1 14 20 28 38 50 64
%e A289762 81 65 51 39 29 21 15 11 9 9 11 15 21 29 39 51 65 81
%e A289762 100 82 66 52 40 30 22 16 12 10 10 12 16 22 30 40 52 66 82 100
%t A289762 Table[(m + 1 - k)^2 + k - 1, {m, 0, 10}, {k, 2 m}] /. {} -> {0} // Flatten (* _Michael De Vlieger_, Jul 12 2017 *)
%o A289762 (PARI) T(m,k) = (m+1-k)^2+k-1 \\ _Charles R Greathouse IV_, Jul 12 2017
%Y A289762 m(41, k+1) = A060566(n), left and right border gives A000290(n).
%K A289762 nonn,tabf,easy
%O A289762 1,3
%A A289762 _Miquel Cerda_, Jul 12 2017