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%I #24 Jun 24 2017 00:25:12
%S 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,
%T 16,1,2,4,8,16,32,63,114,168,176,112,32,1,2,4,8,16,32,64,127,240,396,
%U 512,464,256,64,1,2,4,8,16,32,64,128,255,494,876,1304,1488,1184,576
%N Triangle a(n,k) (0 <= k <= max(0, 2n-1)) of profile numbers.
%H Reinhard Zumkeller, <a href="/A049063/b049063.txt">Rows n = 0..100 of triangle, flattened</a>
%H A. L. Rosenberg, <a href="http://www.fq.math.ca/Scanned/17-3/rosenberg.pdf">Profile numbers</a>, Fibonacci Quart. 17 (1979), no. 3, 259-264.
%F 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).
%e Triangle starts:
%e 1;
%e 1, 1;
%e 1, 2, 3, 2;
%e 1, 2, 4, 7, 8, 4;
%e 1, 2, 4, 8, 15, 22, 20, 8; ...
%t 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 *)
%o (Haskell)
%o a049063 n k = a049063_tabf !! n !! k
%o a133457_row n = a049063_tabf !! n
%o a049063_tabf = [1] : iterate f [1, 1] where
%o f row = 1 : 2 : zipWith (+) ( map (* 2) row) ((tail row) ++ [0])
%o -- _Reinhard Zumkeller_, Feb 12 2013
%K nonn,easy,nice,tabf
%O 0,5
%A _N. J. A. Sloane_
%E More terms from _James A. Sellers_
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