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 A376484 #80 Jun 01 2025 03:20:30
%S A376484 0,1,0,2,3,0,3,5,9,0,4,7,15,27,0,5,9,21,50,81,0,6,11,27,70,175,243,0,
%T A376484 7,13,33,90,245,625,729,0,8,15,39,110,315,882,2250,2187,0,9,17,45,130,
%U A376484 385,1134,3234,8125,6561,0,10,19,51,150,455,1386,4158,12005,29375,19683,0
%N A376484 Array read by ascending antidiagonals: A(n,k)=4^k*Sum_{j=1..n} sin(2*j*Pi/(2*n+1))^(2*k).
%C A376484 It is only a conjecture that A(n,k) is always an integer.
%C A376484 It appears that A(n,k) is divisible by 2*n+1 when n, k are positive integers.
%e A376484 For n = 0 to 10 and k = 0 to 10, A(n, k) shows as below :
%e A376484 0 0 0 0 0 0 0 0 0 0 0
%e A376484 1 3 9 27 81 243 729 2187 6561 19683 59049
%e A376484 2 5 15 50 175 625 2250 8125 29375 106250 384375
%e A376484 3 7 21 70 245 882 3234 12005 44933 169099 638666
%e A376484 4 9 27 90 315 1134 4158 15444 57915 218781 831222
%e A376484 5 11 33 110 385 1386 5082 18876 70785 267410 1016158
%e A376484 6 13 39 130 455 1638 6006 22308 83655 316030 1200914
%e A376484 7 15 45 150 525 1890 6930 25740 96525 364650 1385670
%e A376484 8 17 51 170 595 2142 7854 29172 109395 413270 1570426
%e A376484 9 19 57 190 665 2394 8778 32604 122265 461890 1755182
%e A376484 10 21 63 210 735 2646 9702 36036 135135 510510 1939938
%o A376484 (C++) double gen(int n, int m) {
%o A376484 double s = 0, d = 1;
%o A376484 for(int i = 1; i <= m; i++) d *= 4;
%o A376484 for(int i = 1; i <= n; i++) {
%o A376484 double v = 1;
%o A376484 for(int j = 1; j <= 2 * m; j++) v *= sin(2 * i * M_PI / (2 * n + 1));
%o A376484 s += v * d;
%o A376484 }
%o A376484 return s;
%o A376484 }
%o A376484 (PARI) A(n,k) = 4^k*sum(j=1,n,(sin(2*j*Pi/(2*n+1)))^(2*k))
%Y A376484 Conjectures: This array is related to existing sequences as follows: (Start)
%Y A376484 Rows: A000004, A000244, A020876, A322459 (with alternate signs).
%Y A376484 Columns: A001477, A005408, A016945.
%Y A376484 Main Diagonals: A033876.
%Y A376484 A(0,k) = A000004, A(1,k) = A000244, A(2,k) = A020876, A(3,k) = (-1)^k * A322459 (First 4 rows of the array).
%Y A376484 A(n,0) = A001477(n > 0), A(n,1) = A005408(n > 0), A(n,2) = A016945(n > 0) (First 3 columns of the array).
%Y A376484 A(n,n) = A033876(n > 0) (Main diagonal from top left corner). (End)
%K A376484 nonn,tabl
%O A376484 0,4
%A A376484 _Cheng-Jun Li_, Sep 24 2024