A091435 Array T(n,k) = n*(n+k), read by antidiagonals.
0, 1, 0, 4, 2, 0, 9, 6, 3, 0, 16, 12, 8, 4, 0, 25, 20, 15, 10, 5, 0, 36, 30, 24, 18, 12, 6, 0, 49, 42, 35, 28, 21, 14, 7, 0, 64, 56, 48, 40, 32, 24, 16, 8, 0, 81, 72, 63, 54, 45, 36, 27, 18, 9, 0, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0, 121, 110, 99, 88, 77, 66, 55, 44, 33, 22, 11, 0
Offset: 0
Examples
Table begins 0; 1, 0; 4, 2, 0; 9, 6, 3, 0; 16, 12, 8, 4, 0; 25, 20, 15, 10, 5, 0; 36, 30, 24, 18, 12, 6, 0; ... a(5,3) = 40 because 5 * (5 + 3) = 5 * 8 = 40.
Links
- Muniru A Asiru, Table of n, a(n) for n = 0..5150 (rows n = 0..100,flattened)
- P. De Geest, Palindromic Quasipronics of the form n(n+x)
Crossrefs
Columns: a(n, 0) = A000290(n), a(n, 1) = A002378(n), a(n, 2) = A005563(n), a(n, 3) = A028552(n), a(n, 4) = A028347(n+2), a(n, 5) = A028557(n), a(n, 6) = A028560(n), a(n, 7) = A028563(n), a(n, 8) = A028566(n). Diagonals: a(n, n-4) = A054000(n-1), a(n, n-3) = A014107(n), a(n, n-2) = A046092(n-1), a(n, n-1) = A000384(n), a(n, n) = A001105(n), a(n, n+1) = A014105(n), a(n, n+2) = A046092(n), a(n, n+3) = A014106(n), a(n, n+4) = A054000(n+1), a(n, n+5) = A033537(n). Also note that the sums of the antidiagonals = A002411.
Programs
-
GAP
Flat(List([0..11],j->List([0..j],i->j*(j-i)))); # Muniru A Asiru, Sep 11 2018
-
Maple
seq(seq((j-i)*j,i=0..j),j=0..14);
-
Mathematica
Table[# (# + k) &[m - k], {m, 0, 11}, {k, 0, m}] // Flatten (* Michael De Vlieger, Oct 15 2018 *)
Formula
G.f.: x*(1+x-2*x^2*y)/((1-x*y)^2*(1-x)^3). - Vladeta Jovovic, Mar 05 2004
Extensions
More terms from Emeric Deutsch, Mar 15 2004