|
| |
|
|
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.
|
|
5
| |
|
|
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
(list; graph; refs; listen; history; internal format)
|
|
|
|
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 (Deutsch)
|
|
|
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}]] (* From 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 A094440 A093736
Adjacent sequences: A099956 A099957 A099958 * A099960 A099961 A099962
|
|
|
KEYWORD
| nonn,tabf,nice,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 13 2004, following a suggestion made by Douglas G. Rogers, Mar 10, 2003
|
|
|
EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 16 2004
|
| |
|
|
