A091435 - OEIS

%I #31 Aug 11 2024 14:41:34

%S 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,

%T 49,42,35,28,21,14,7,0,64,56,48,40,32,24,16,8,0,81,72,63,54,45,36,27,

%U 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

%N Array T(n,k) = n*(n+k), read by antidiagonals.

%H Muniru A Asiru, <a href="/A091435/b091435.txt">Table of n, a(n) for n = 0..5150</a> (rows n = 0..100,flattened)

%H P. De Geest, <a href="https://www.worldofnumbers.com/consemor.htm">Palindromic Quasipronics of the form n(n+x)</a>

%F G.f.: x*(1+x-2*x^2*y)/((1-x*y)^2*(1-x)^3). - _Vladeta Jovovic_, Mar 05 2004

%e Table begins

%e    0;

%e    1,  0;

%e    4,  2,  0;

%e    9,  6,  3,  0;

%e   16, 12,  8,  4,  0;

%e   25, 20, 15, 10,  5,  0;

%e   36, 30, 24, 18, 12,  6,  0;

%e   ...

%e a(5,3) = 40 because 5 * (5 + 3) = 5 * 8 = 40.

%p seq(seq((j-i)*j,i=0..j),j=0..14);

%t Table[# (# + k) &[m - k], {m, 0, 11}, {k, 0, m}] // Flatten (* _Michael De Vlieger_, Oct 15 2018 *)

%o (GAP) Flat(List([0..11],j->List([0..j],i->j*(j-i)))); # _Muniru A Asiru_, Sep 11 2018

%Y 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.

%Y Cf. A056536, A056537, A082156.

%K easy,nonn,tabl

%O 0,4

%A _Ross La Haye_, Mar 02 2004

%E More terms from _Emeric Deutsch_, Mar 15 2004