A049063 Triangle a(n,k) (0 <= k <= max(0, 2n-1)) of profile numbers.

1, 1, 1, 1, 2, 3, 2, 1, 2, 4, 7, 8, 4, 1, 2, 4, 8, 15, 22, 20, 8, 1, 2, 4, 8, 16, 31, 52, 64, 48, 16, 1, 2, 4, 8, 16, 32, 63, 114, 168, 176, 112, 32, 1, 2, 4, 8, 16, 32, 64, 127, 240, 396, 512, 464, 256, 64, 1, 2, 4, 8, 16, 32, 64, 128, 255, 494, 876, 1304, 1488, 1184, 576

Offset

0,5

Links

Reinhard Zumkeller, Rows n = 0..100 of triangle, flattened

A. L. Rosenberg, Profile numbers, Fibonacci Quart. 17 (1979), no. 3, 259-264.

Formula

a(n+1, k+1) = a(n, k)+2*a(n, k-1), k>0; a(n, 0)=1, a(1, 1)=1, a(n, 1)=2, a(n, n)=2^(n-1).

Example

Triangle starts:
  1;
  1, 1;
  1, 2, 3, 2;
  1, 2, 4, 7,  8,  4;
  1, 2, 4, 8, 15, 22, 20, 8; ...

Mathematica

a[n_ /; n >= 1, 0] = 1; a[1, 1] = 1; a[n_ /; n > 1, 1] = 2; a[1, k_ /; k > 1] = 0; a[0, 0] = 1; a[n_, k_ /; k > 0] := a[n, k] = a[n-1, k-1] + 2 a[n-1, k-2]; a[_, _] = 0; Table[a[n, k], {n, 0, 8}, {k, 0, Max[0, 2n-1]}] // Flatten (* Jean-François Alcover, Oct 19 2016 *)

Prog

(Haskell)
a049063 n k = a049063_tabf !! n !! k
a133457_row n = a049063_tabf !! n
a049063_tabf = [1] : iterate f [1, 1] where
   f row = 1 : 2 : zipWith (+) ( map (* 2) row) ((tail row) ++ [0])
-- Reinhard Zumkeller, Feb 12 2013

Crossrefs

Sequence in context: A222173 A301368 A198242 * A120894 A134819 A135267

Adjacent sequences: A049060 A049061 A049062 * A049064 A049065 A049066

Keyword

nonn,easy,nice,tabf

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers

Status

approved