This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A059283 #10 Oct 11 2013 04:31:00
%S A059283 1,0,1,0,2,3,0,2,8,11,0,2,14,36,47,0,2,20,78,172,219,0,2,26,138,424,
%T A059283 862,1081,0,2,32,216,856,2314,4476,5557,0,2,38,312,1522,5116,12768,
%U A059283 23882,29439,0,2,44,426,2476,9970,30168,71294,130172,159611,0,2,50,558
%N A059283 Triangle T(n,k) (0<= k <=n) read by rows. Left edge is 1, 0, 0, ... Otherwise each entry is sum of entry to left, entries immediately above it to left and right and entry directly above it 2 rows back.
%H A059283 Reinhard Zumkeller, <a href="/A059283/b059283.txt">Rows n = 0..120 of triangle, flattened</a>
%F A059283 T(0, 0)=1; T(n, 0)=0, n>0; T(n, k)=T(n, k-1)+T(n-1, k-1)+T(n-1, k)+T(n-2, k-1), n, k>0
%F A059283 G.f. for T(n, k): ((1+2*w+w^2)*z^2+(-1-2*w-w^2)*z-w*(-3*w^2-6*w+1)^(1/2)+2*w)/(1+w)^2/((1+w)*z^2+(w-1)*z+w) (expand first as series in z, then in w).
%e A059283 1; 0,1; 0,2,3; 0,2,8,11; 0,2,14,36,47; ... [36 = 14 + 8 + 11 + 3 for example].
%t A059283 t[0, 0] = 1; t[_, 0] = 0; t[n_, k_] /; 0 <= k <= n := t[n, k] = t[n, k-1] + t[n-1, k-1] + t[n-1, k] + t[n-2, k-1]; t[_, _] = 0; Table[t[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Oct 11 2013 *)
%o A059283 (Haskell)
%o A059283 a059283 n k = a059283_tabl !! n !! k
%o A059283 a059283_row n = a059283_tabl !! n
%o A059283 a059283_tabl = [1] : [0,1] : f [1] [0,1] where
%o A059283 f us vs = ws : f vs ws where
%o A059283 ws = scanl1 (+) $ zipWith (+)
%o A059283 ([0]++us++[0]) $ zipWith (+) ([0]++vs) (vs++[0])
%o A059283 -- _Reinhard Zumkeller_, Apr 17 2013
%Y A059283 Right edge is A059284. Cf. A059226.
%Y A059283 Cf. A224729 (central terms), A122542.
%K A059283 nonn,tabl,easy,nice
%O A059283 0,5
%A A059283 _N. J. A. Sloane_, Jan 24 2001
%E A059283 More terms from Larry Reeves (larryr(AT)acm.org), Jan 25 2001