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 A098832 #6 Aug 01 2022 08:11:59
%S A098832 1,3,3,6,8,2,10,15,5,5,15,24,9,12,3,21,35,14,21,7,7,28,48,20,32,12,16,
%T A098832 4,36,63,27,45,18,27,9,9,45,80,35,60,25,40,15,20,5,55,99,44,77,33,55,
%U A098832 22,33,11,11,66,120,54,96,42,72,30,48,18,24,6,78,143,65,117,52,91,39,65,26,39,13,13
%N A098832 Square array read by antidiagonals: even-numbered rows of the table are of the form n*(n+m) and odd-numbered rows are of the form n*(n+m)/2.
%C A098832 The rows of this table and that in A098737 are related. Given a function f = n/( 1 + (1+n) mod(2) ), row n of A098737 can be derived from row n of T by multiplying the latter by f(n); row n of T can be derived from row n of A098737 by dividing the latter by f(n).
%H A098832 G. C. Greubel, <a href="/A098832/b098832.txt">Antidiagonals n = 1..50, flattened</a>
%F A098832 Item m of row n of T is given (in infix form) by: n T m = n * (n + m) / (1 + m (mod 2)). E.g. Item 4 of row 3 of T: 3 T 4 = 14.
%F A098832 From _G. C. Greubel_, Jul 31 2022: (Start)
%F A098832 A(n, k) = (1/4)*(3 + (-1)^n)*k*(k+n) (array).
%F A098832 T(n, k) = (1/4)*(3 + (-1)^k)*(n+1)*(n-k+1) (antidiagonal triangle).
%F A098832 Sum_{k=1..n} T(n, k) = (1/8)*(n+1)*( (3*n-1)*(n+1) + (1+(-1)^n)/2 ).
%F A098832 T(2*n-1, n) = A181900(n).
%F A098832 T(2*n+1, n) = 2*A168509(n+1). (End)
%e A098832 Array begins as:
%e A098832 1, 3, 6, 10, 15, 21, 28, 36, 45 ... A000217;
%e A098832 3, 8, 15, 24, 35, 48, 63, 80, 99 ... A005563;
%e A098832 2, 5, 9, 14, 20, 27, 35, 44, 54 ... A000096;
%e A098832 5, 12, 21, 32, 45, 60, 77, 96, 117 ... A028347;
%e A098832 3, 7, 12, 18, 25, 33, 42, 52, 63 ... A027379;
%e A098832 7, 16, 27, 40, 55, 72, 91, 112, 135 ... A028560;
%e A098832 4, 9, 15, 22, 30, 39, 49, 60, 72 ... A055999;
%e A098832 9, 20, 33, 48, 65, 84, 105, 128, 153 ... A028566;
%e A098832 5, 11, 18, 26, 35, 45, 56, 68, 81 ... A056000;
%e A098832 Antidiagonals begin as:
%e A098832 1;
%e A098832 3, 3;
%e A098832 6, 8, 2;
%e A098832 10, 15, 5, 5;
%e A098832 15, 24, 9, 12, 3;
%e A098832 21, 35, 14, 21, 7, 7;
%e A098832 28, 48, 20, 32, 12, 16, 4;
%e A098832 36, 63, 27, 45, 18, 27, 9, 9;
%e A098832 45, 80, 35, 60, 25, 40, 15, 20, 5;
%e A098832 55, 99, 44, 77, 33, 55, 22, 33, 11, 11;
%t A098832 A098832[n_, k_]:= (1/4)*(3+(-1)^k)*(n+1)*(n-k+1);
%t A098832 Table[A098832[n,k], {n,15}, {k,n}]//Flatten (* _G. C. Greubel_, Jul 31 2022 *)
%o A098832 (Magma)
%o A098832 A098832:= func< n,k | (1/4)*(3+(-1)^k)*(n+1)*(n-k+1) >;
%o A098832 [A098832(n,k): k in [1..n], n in [1..15]]; // _G. C. Greubel_, Jul 31 2022
%o A098832 (SageMath)
%o A098832 def A098832(n,k): return (1/4)*(3+(-1)^k)*(n+1)*(n-k+1)
%o A098832 flatten([[A098832(n,k) for k in (1..n)] for n in (1..15)]) # _G. C. Greubel_, Jul 31 2022
%Y A098832 Row m of array: A000217 (m=1), A005563 (m=2), A000096 (m=3), A028347 (m=4), A027379 (m=5), A028560 (m=6), A055999 (m=7), A028566 (m=8), A056000 (m=9), A098603 (m=10), A056115 (m=11), A098847 (m=12), A056119 (m=13), A098848 (m=14), A056121 (m=15), A098849 (m=16), A056126 (m=17), A098850 (m=18), A051942 (m=19).
%Y A098832 Column m of array: A026741 (m=1), A022998 (m=2), A165351 (m=3).
%Y A098832 Cf. A098737, A168509, A181900.
%K A098832 easy,nonn,tabl
%O A098832 1,2
%A A098832 Eugene McDonnell (eemcd(AT)mac.com), Nov 02 2004
%E A098832 Missing terms added by _G. C. Greubel_, Jul 31 2022