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 A095802 #19 Jan 09 2020 03:57:01 %S A095802 1,-2,9,3,-6,25,-4,15,-10,49,5,-12,35,-14,81,-6,21,-20,63,-18,121,7, %T A095802 -18,45,-28,99,-22,169,-8,27,-30,77,-36,143,-26,225,9,-24,55,-42,117, %U A095802 -44,195,-30,289,-10,33,-40,91,-54,165,-52,255,-34,361,11,-30,65,-56,135,-66,221,-60,323,-38,441,-12,39,-50,105,-72,187,-78,285,-68,399,-42,529 %N A095802 Upper right triangular matrix T^2, where T(i,j) = (-1)^i*(1-2*i) for 1 <= i <= j. %C A095802 Equivalently, (lower left) triangle M^2 = transpose(T)^2. The following description refers to the lower triangular version, but OEIS's "TABL" link displays the values more appropriately as an upper right triangle. - _M. F. Hasler_, Apr 18 2009 %C A095802 For n rows, use matrices in each row from the sequence 1, -3, 5, -7, ... (filling in with zeros except for the n-th row). Let the matrix = M, then square and delete the zeros. For example, the 3-row generator would be [1 0 0 / 1 -3 0 / 1 -3 5] = M. The nonzero elements of M^2 give the first 6 terms of the sequence. %F A095802 Diagonal elements are the odd squares: a(k(k+1)/2)=(2k+1)^2. First element in row k is (-1)^k*k. - _M. F. Hasler_, Apr 18 2009 %e A095802 The matrix %e A095802 [ 1 0 0 0 ...] %e A095802 [ 1 -3 0 0 ...] %e A095802 [ 1 -3 5 0 ...] %e A095802 [ 1 -3 5 -7 ...] %e A095802 squared yields %e A095802 [ +1 0 0 0 ...] %e A095802 [ -2 +9 0 0 ...] %e A095802 [ +3 -6 25 0 ...] %e A095802 [ -4 15 -10 49 ...]; the lower left triangle gives this sequence: 1; -2, 9; 3, -6, 25; ... %o A095802 (PARI) T=matrix(12,12,i,j,if(j>=i,(-1)^i*(1-2*i)))^2; concat(vector(#T,i,vecextract(T[,i],2^i-1))) \\ _M. F. Hasler_, Apr 18 2009 %Y A095802 Row sums with signs as shown = A002412, Hexagonal pyramidal numbers: (1, 7, 22, 50, 95, ...). %Y A095802 Cf. A002412. %K A095802 sign,tabl %O A095802 1,2 %A A095802 _Gary W. Adamson_, Jun 07 2004 %E A095802 Edited and extended by _M. F. Hasler_, Apr 18 2009