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 A059226 Triangle T(n,k) (0 <= k <= n) read by rows: top entry is 1, all other rows begin with 0; typical entry is sum of entry to left plus sum of all entries above it in the triangle. 12
 1, 0, 1, 0, 2, 4, 0, 4, 12, 18, 0, 8, 32, 70, 94, 0, 16, 80, 224, 426, 544, 0, 32, 192, 648, 1536, 2708, 3370, 0, 64, 448, 1760, 4920, 10596, 17846, 21878, 0, 128, 1024, 4576, 14624, 36552, 74040, 121014, 146924, 0, 256, 2304, 11520, 41248 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Variant of Boustrophedon transform applied to 1, 0, 0, 0, ... LINKS Vincenzo Librandi, Rows n = 0..100, flattened EXAMPLE Triangle begins:   1;   0,   1;   0,   2,   4;   0,   4,  12,  18;   0,   8,  32,  70,  94;   0,  16,  80, 224, 426, 544;   ... T(4,3) = 70 because it is the sum of the entry to the left (32) plus the sum of all the entries above position (4,3), which give 1 + 0 + 1 + 2 + 4 + 12 + 18. MAPLE T := proc(i, j) option remember; local r, s, t1; if i=0 and j=0 then RETURN(1); fi; if j=0 then RETURN(0); fi; t1 := T(i, j-1); for r from 0 to i-j do for s from 0 to j do if r+s <> i then t1 := t1+T(r+s, s); fi; od: od: RETURN(t1); end; # n-th row is T(n, 0), T(n, 1), ..., T(n, n) To get the triangle formed when the left diagonal has a single 1 in position k: T := proc(i, j, k) option remember; local r, s, t1; if i < k then RETURN(0); fi; if i = k then RETURN(1); fi; if j = 0 then RETURN(0); fi; t1 := T(i, j-1, k); for r from 0 to i-j do for s from 0 to j do if r+s <> i then t1 := t1+T(r+s, s, k); fi; od: od: t1; end; MATHEMATICA T [i_, j_] := T[i, j] = Module[{r, s, t1}, If[i == 0 && j == 0, Return[1]]; If[j == 0, Return[0]]; t1 = T[i, j-1]; For[r = 0, r <= i-j, r++, For[s = 0, s <= j, s++, If[r+s != i, t1 = t1 + T[r+s, s]]]]; Return[t1]]; Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Dec 26 2013, translated from Maple *) CROSSREFS Diagonals give A000079, A001787, A059224, A059229. Final entries in each row give A059227. Row sums give A059228. Cf. A059271. Sequence in context: A341862 A256487 A079985 * A221655 A221087 A279580 Adjacent sequences:  A059223 A059224 A059225 * A059227 A059228 A059229 KEYWORD nonn,easy,tabl,nice AUTHOR N. J. A. Sloane, Jan 19 2001 STATUS approved

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Last modified January 18 00:52 EST 2022. Contains 350410 sequences. (Running on oeis4.)