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 A195151 #20 Oct 26 2023 10:10:06 %S A195151 0,1,0,0,1,0,3,1,1,0,0,3,2,1,0,5,2,3,3,1,0,0,5,4,3,4,1,0,7,3,5,6,3,5, %T A195151 1,0,0,7,6,5,8,3,6,1,0,9,4,7,9,5,10,3,7,1,0,0,9,8,7,12,5,12,3,8,1,0, %U A195151 11,5,9,12,7,15,5,14,3,9,1,0,0,11,10,9,16,7 %N A195151 Square array read by antidiagonals upwards: T(n,k) = n*((k-2)*(-1)^n+k+2)/4, n >= 0, k >= 0. %C A195151 Also square array T(n,k) read by antidiagonals in which column k lists the multiples of k and the odd numbers interleaved, n>=0, k>=0. Also square array T(n,k) read by antidiagonals in which if n is even then row n lists the multiples of (n/2), otherwise if n is odd then row n lists a constant sequence: the all n's sequence. Partial sums of the numbers of column k give the column k of A195152. Note that if k >= 1 then partial sums of the numbers of the column k give the generalized m-gonal numbers, where m = k + 4. %C A195151 All columns are multiplicative. - _Andrew Howroyd_, Jul 23 2018 %e A195151 Array begins: %e A195151 . 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,... %e A195151 . 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,... %e A195151 . 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,... %e A195151 . 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,... %e A195151 . 0, 2, 4, 6, 8, 10, 12, 14, 16, 18,... %e A195151 . 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,... %e A195151 . 0, 3, 6, 9, 12, 15, 18, 21, 24, 27,... %e A195151 . 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,... %e A195151 . 0, 4, 8, 12, 16, 20, 24, 28, 32, 36,... %e A195151 . 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,... %e A195151 . 0, 5, 10, 15, 20, 25, 30, 35, 40, 45,... %e A195151 ... %o A195151 (PARI) T(n,k) = n*((k-2)*(-1)^n+k+2)/4 \\ _Andrew Howroyd_, Jul 23 2018 %Y A195151 Rows: A000004, A000012, A001477, A010701, A005843, A010716, A008585, A010727, A008586, A010734, A008587. %Y A195151 Columns k: A026741 (k=1), A001477 (k=2), zero together with A080512 (k=3), A022998 (k=4), A195140 (k=5), zero together with A165998 (k=6), A195159 (k=7), A195161 (k=8), A195312 k=(9), A195817 (k=10), A317311 (k=11), A317312 (k=12), A317313 (k=13), A317314 k=(14), A317315 (k=15), A317316 (k=16), A317317 (k=17), A317318 (k=18), A317319 k=(19), A317320 (k=20), A317321 (k=21), A317322 (k=22), A317323 (k=23), A317324 k=(24), A317325 (k=25), A317326 (k=26). %K A195151 nonn,tabl,mult %O A195151 0,7 %A A195151 _Omar E. Pol_, Sep 14 2011