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 A176282 #18 Jun 30 2025 00:51:39
%S A176282 1,1,1,1,4,1,1,9,9,1,1,16,21,16,1,1,25,37,37,25,1,1,36,57,64,57,36,1,
%T A176282 1,49,81,97,97,81,49,1,1,64,109,136,145,136,109,64,1,1,81,141,181,201,
%U A176282 201,181,141,81,1,1,100,177,232,265,276,265,232,177,100,1
%N A176282 Triangle T(n,k) = 1 + A000330(n) - A000330(k) - A000330(n-k), read by rows.
%C A176282 Not summing squares but summing integers implied by the definition (i.e., not using A000330 but A000217) gives A077028.
%C A176282 Row sums = {1, 2, 6, 20, 55, 126, 252, 456, 765, 1210, 1826, ...} = (n+1)*(n+2)*(n^2-2*n+3)/6.
%H A176282 G. C. Greubel, <a href="/A176282/b176282.txt">Rows n = 0..100 of triangle, flattened</a>
%F A176282 T(n,k) = T(n,n-k).
%F A176282 T(n,k) = 1 + k*(n+1)*(n-k). - _G. C. Greubel_, Nov 24 2019
%e A176282 Triangle begins as:
%e A176282 1;
%e A176282 1, 1;
%e A176282 1, 4, 1;
%e A176282 1, 9, 9, 1;
%e A176282 1, 16, 21, 16, 1;
%e A176282 1, 25, 37, 37, 25, 1;
%e A176282 1, 36, 57, 64, 57, 36, 1;
%e A176282 1, 49, 81, 97, 97, 81, 49, 1;
%e A176282 1, 64, 109, 136, 145, 136, 109, 64, 1;
%e A176282 1, 81, 141, 181, 201, 201, 181, 141, 81, 1;
%e A176282 1, 100, 177, 232, 265, 276, 265, 232, 177, 100, 1;
%p A176282 seq(seq(1 + k*(n+1)*(n-k), k=0..n), n=0..12); # _G. C. Greubel_, Nov 24 2019
%t A176282 (* Set of sequences q=1..10. This sequence is q=2. *)
%t A176282 f[n_, k_, q_]:= f[n, k, q] = 1 + Sum[i^q, {i,0,n}] - Sum[i^q, {i,0,k}] - Sum[i^q, {i,0,n-k}]; Table[Flatten[Table[f[n, k, q], {n,0,12}, {k,0,n}]], {q,1,10}]
%t A176282 (* Second program *)
%t A176282 Table[1 + k*(n+1)*(n-k), {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, Nov 24 2019 *)
%o A176282 (PARI) T(n,k) = 1 + k*(n+1)*(n-k); \\ _G. C. Greubel_, Nov 24 2019
%o A176282 (Magma) [1 + k*(n+1)*(n-k): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Nov 24 2019
%o A176282 (Sage) [[1 + k*(n+1)*(n-k) for k in (0..n)] for n in (0..12)] # _G. C. Greubel_, Nov 24 2019
%o A176282 (GAP) Flat(List([0..12], n-> List([0..n], k-> 1 + k*(n+1)*(n-k) ))); # _G. C. Greubel_, Nov 24 2019
%Y A176282 Cf. A077028.
%K A176282 nonn,tabl,easy
%O A176282 0,5
%A A176282 _Roger L. Bagula_, Apr 14 2010
%E A176282 Edited by _R. J. Mathar_, May 03 2013