A099959 Triangle read by rows: Each row is constructed by forming the partial sums of the previous row, reading from the right and at every other row repeating the final term.

1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 6, 8, 8, 14, 17, 17, 17, 34, 48, 56, 56, 104, 138, 155, 155, 155, 310, 448, 552, 608, 608, 1160, 1608, 1918, 2073, 2073, 2073, 4146, 6064, 7672, 8832, 9440, 9440, 18272, 25944, 32008, 36154, 38227, 38227, 38227, 76454, 112608

Offset

0,6

Comments

...

Links

Reinhard Zumkeller, Rows n = 0..119 of triangle, flattened

Example

Triangle begins
   1;
   1,
   1,   1;
   1,   2,
   2,   3,   3;
   3,   6,   8,
   8,  14,  17,  17;
  17,  34,  48,  56,
  56, 104, 138, 155, 155;

Maple

with(linalg):rev:=proc(a) local n, p; n:=vectdim(a): p:=i->a[n+1-i]: vector(n, p) end: ps:=proc(a) local n, q; n:=vectdim(a): q:=i->sum(a[j], j=1..i): vector(n, q) end: pss:=proc(a) local n, q; n:=vectdim(a): q:=proc(i) if i<=n then sum(a[j], j=1..i) else sum(a[j], j=1..n) fi end: vector(n+1, q) end: R[0]:=vector(1, 1): for n from 1 to 18 do if n mod 2 = 1 then R[n]:=ps(rev(R[n-1])) else R[n]:=pss(rev(R[n-1])) fi od: for n from 0 to 18 do evalm(R[n]) od; # program yields the successive rows # Emeric Deutsch, Nov 16 2004

Mathematica

row[0] = row[1] = {1}; row[n_?OddQ] := Accumulate[ Reverse[ row[n-1] ] ]; row[n_?EvenQ] := (r = Accumulate[ Reverse[ row[n-1] ] ]; AppendTo[r, Last[r] ]); Flatten[ Table[ row[n], {n, 0, 13}]] (* Jean-François Alcover, Dec 16 2011 *)

Prog

(Haskell)
a099959 n k = a099959_tabl !! n !! k
a099959_row n = a099959_tabl !! n
a099959_tabl = map snd $ iterate f (False, [1]) where
   f (s, xs) = (not s, if s then zs ++ [last zs] else zs)
     where zs = scanl1 (+) (reverse xs)
-- Reinhard Zumkeller, Dec 28 2011

Crossrefs

First column (and row sums) gives A099960.

If an extra term is added to /every/ row we get A008282. Cf. A099961.

Sequence in context: A080968 A115733 A025496 * A099964 A369302 A363826

Adjacent sequences: A099956 A099957 A099958 * A099960 A099961 A099962

Keyword

nonn,tabf,nice,easy

Author

N. J. A. Sloane, Nov 13 2004

Extensions

More terms from Emeric Deutsch, Nov 16 2004

Status

approved