A048505 Array T read by antidiagonals, n-th difference of (T(k,n),T(k,n-1),...,T(k,0)) is (k+n)^2, for n=1,2,3,...; k=0,1,2,...

1, 2, 1, 7, 5, 1, 25, 18, 10, 1, 81, 56, 35, 17, 1, 241, 160, 101, 58, 26, 1, 673, 432, 269, 160, 87, 37, 1, 1793, 1120, 685, 408, 233, 122, 50, 1, 4609, 2816, 1693, 1000, 577, 320, 163, 65, 1, 11521, 6912, 4093, 2392, 1377, 776, 421

Offset

0,2

Links

Table of n, a(n) for n=0..51.

Formula

T(k, n) = (n^2 + (4k+1)n + (2k)^2) * 2^(n-2) - k^2 + 1. - Ralf Stephan, Feb 05 2004

Example

  1,   1,   1,   1,   1,   1,   1,   1,   1,   1,   1,   1,   1,...
   2,   5,  10,  17,  26,  37,  50,  65,  82, 101, 122, 145, 170,...
   7,  18,  35,  58,  87, 122, 163, 210, 263, 322, 387, 458, 535,...
  25,  56, 101, 160, 233, 320, 421, 536, 665, 808, 965,1136,1321,...
  81, 160, 269, 408, 577, 776,1005,1264,1553,1872,2221,2600,3009,...

Maple

A048505 := proc(n, k)
    (n^2 + (4*k+1)*n + (2*k)^2) * 2^(n-2) - k^2 + 1 ;
end proc:
seq(seq( A048505(d-k, k), k=0..d), d=0..12) ;

Crossrefs

Column 2 = (1, 5, 18, 56, 160, ...) = A001793; A048507 (column 3), A048508 (column 4), A048514 (antidiagonal sums).

Sequence in context: A019642 A339000 A248811 * A124821 A104030 A206533

Adjacent sequences: A048502 A048503 A048504 * A048506 A048507 A048508

Keyword

nonn,tabl,changed

Author

Clark Kimberling

Status

approved