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 A368415 #15 Jan 20 2024 09:42:32 %S A368415 1,1,1,2,2,1,2,4,3,1,3,7,11,6,1,3,11,26,31,11,1,4,16,53,103,92,22,1,4, %T A368415 22,93,261,410,274,43,1,5,29,151,556,1303,1639,821,86,1,5,37,228,1051, %U A368415 3333,6511,6554,2461,171,1,6,46,329,1821,7354,19996,32553,26215,7382,342,1,6,56,455,2953 %N A368415 Array read by ascending antidiagonals. A(n, k) = floor((n^k + 3)*(n/(2*n + 2))). %C A368415 Let p be an odd prime number, then A(p, k) is the number of distinct quadratic residues mod p^k. Let m = p1^k1^*p2^k2*..*pz^kz with p1..pz odd primes, then A(p1, k1)*A(p2, k2)*..*A(pz, kz) is the number of distinct quadratic residues mod m. For 2^t*m is floor((2^t+10)*(1/6))*A(p1, k1)*A(p2, k2)*..*A(pz, kz) the number of distinct quadratic residues mod 2^t*m. %F A368415 A(n, k) = n*A(n, k-1) + A(n, k-2) - n*A(n, k-3), for k > 2 and A(n, 0) = 1. %F A368415 A(1, k) = 1. %F A368415 A(2, k) = A005578(k). %F A368415 A(3, k) = A039300(k). %F A368415 A(4, k) = A363773(k). %F A368415 A(5, k) = A039302(k). %F A368415 A(7, k) = A039304(k). %F A368415 A(8, k) = A172241(k+1)+1. %F A368415 A(n, 2) = A000124(n-1), for n > 0. %e A368415 The array A(n, k) begins: %e A368415 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 %e A368415 1, 2, 3, 6, 11, 22, 43, 86, 171, 342 %e A368415 2, 4, 11, 31, 92, 274, 821, 2461, 7382, 22144 %e A368415 2, 7, 26, 103, 410, 1639, 6554, 26215, 104858, 419431 %e A368415 3, 11, 53, 261, 1303, 6511, 32553, 162761, 813803, 4069011 %e A368415 3, 16, 93, 556, 3333, 19996, 119973, 719836, 4319013, 25914076 %e A368415 4, 22, 151, 1051, 7354, 51472, 360301, 2522101, 17654704, 123582922 %e A368415 4, 29, 228, 1821, 14564, 116509, 932068, 7456541, 59652324, 477218589 %e A368415 5, 37, 323, 2953, 26573, 239149, 2152337, 19371025, 174339221, 1569052981 %e A368415 5, 46, 455, 4546, 45455, 454546, 4545455, 45454546, 454545455, 4545454546 %o A368415 (PARI) A(n, k) = (n^(k+1)+n*3)\(2*n+2) %Y A368415 Cf. A000124, A005578, A039300, A039302, A039304, A172241, A363773. %K A368415 nonn,tabl %O A368415 1,4 %A A368415 _Thomas Scheuerle_, Dec 23 2023