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Search: id:A059226
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| A059226 |
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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. |
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12
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| 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; listen)
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OFFSET
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0,5
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COMMENT
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Variant of Boustrophedon transform applied to 1,0,0,0,...
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LINKS
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Index entries for sequences related to boustrophedon transform
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EXAMPLE
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1; 0,1; 0,2,4; 0,4,12,18; 0,8,32,70,94; ...
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.
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MAPLE
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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;
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CROSSREFS
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Diagonals give A000079, A001787, A059224, A059229. Final entries in each row give A059227. Row sums give A059228. Cf. A059271.
Sequence in context: A115368 A086932 A079985 this_sequence A097666 A144810 A002652
Adjacent sequences: A059223 A059224 A059225 this_sequence A059227 A059228 A059229
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KEYWORD
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nonn,easy,tabl,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jan 19 2001
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