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 A131804 Antidiagonal sums of triangular array T: T(j,k) = -(k+1)/2 for odd k, T(j,k) = 0 for k = 0, T(j,k) = j+1-k/2 for even k > 0; 0 <= k <= j. 2
 0, 0, -1, -1, 1, 2, 1, 2, 6, 8, 7, 9, 15, 18, 17, 20, 28, 32, 31, 35, 45, 50, 49, 54, 66, 72, 71, 77, 91, 98, 97, 104, 120, 128, 127, 135, 153, 162, 161, 170, 190, 200, 199, 209, 231, 242, 241, 252, 276, 288, 287, 299, 325, 338, 337, 350, 378, 392, 391, 405, 435, 450 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS T is obtained by replacing the values of the second, fourth, sixth, ... column of the triangular array defined in A129819 by the corresponding negative values. Interleaving of A000384, A001105, A056220 and A014107 (starting at the second term). Main diagonal of T is in A001057, row sums are in A131805. LINKS FORMULA a(0) = 0, a(1) = 0, a(2) = -1, a(3) = -1, a(4) = 1, a(5) = 2, a(6) = 1; for n > 6, a(n) = 3*a(n-1) - 5*a(n-2) + 7*a(n-3) - 7*a(n-4) + 5*a(n-5) - 3*a(n-6) + a(n-7); G.f.: x^2*(-1+2*x-x^2+x^3)/((1-x)^3*(1+x^2)^2). EXAMPLE First seven rows of T are [ 0 ], [ 0, -1 ], [ 0, -1, 2 ], [ 0, -1, 3, -2 ], [ 0, -1, 4, -2, 3 ], [ 0, -1, 5, -2, 4, -3 ], [ 0, -1, 6, -2, 5, -3, 4 ] PROG (MAGMA) m:=62; M:=ZeroMatrix(IntegerRing(), m, m); for j:=1 to m do for k:=2 to j do if k mod 2 eq 0 then M[j, k]:=-k div 2; else M[j, k]:=j-(k div 2); end if; end for; end for; [ &+[ M[j-k+1, k]: k in [1..(j+1) div 2] ]: j in [1..m] ]; (PARI) {for(n=0, 61, r=n%4; k=(n-r)/4; a=if(r==0, k*(2*k-1), if(r==1, 2*k^2, if(r==2, 2*k^2-1, k*(2*k+1)-1))); print1(a, ", "))} CROSSREFS Cf. A129819, A000384 (n*(2*n-1)), A001105 (2*n^2), A056220 (2*n^2-1), A014107 (n*(2*n-3)), A001057, A131805. Sequence in context: A020825 A259992 A110422 * A254198 A246466 A170829 Adjacent sequences:  A131801 A131802 A131803 * A131805 A131806 A131807 KEYWORD sign AUTHOR Klaus Brockhaus, Jul 18 2007 STATUS approved

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Last modified October 21 17:10 EDT 2018. Contains 316427 sequences. (Running on oeis4.)