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A099961 Triangle read by rows: Each row is constructed by forming the partial sums of the previous row, reading from the right and at every third row repeating the final term. 6
1, 1, 1, 1, 1, 2, 2, 3, 3, 5, 5, 5, 10, 13, 13, 23, 28, 28, 51, 64, 64, 64, 128, 179, 207, 207, 386, 514, 578, 578, 1092, 1478, 1685, 1685, 1685, 3370, 4848, 5940, 6518, 6518, 12458, 17306, 20676, 22361, 22361, 43037, 60343, 72801, 79319, 79319, 79319 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

...

LINKS

Reinhard Zumkeller, Rows n=0..120 of triangle, flattened

EXAMPLE

Triangle begins

   1;

   1,

   1,  1;

   1,  2,

   2,  3,

   3,  5,  5;

   5, 10, 13,

  13, 23, 28,

  28, 51, 64, 64;

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 19 do if n mod 3 = 0 or n mod 3 = 1 then R[n]:=ps(rev(R[n-1])) else R[n]:=pss(rev(R[n-1])) fi od: for n from 0 to 19 do evalm(R[n]) od; # program yields the successive rows # Emeric Deutsch, Nov 16 2004

MATHEMATICA

r[0] = {1}; r[n_] := r[n] = Join[ a = Accumulate[ Reverse[r[n-1]]], If[Mod[n, 3] == 2, {Last[a]}, {}]]; Flatten[ Table[r[n], {n, 0, 15}]](* Jean-Fran├žois Alcover, Mar 13 2012 *)

PROG

(Haskell)

a099961 n k = a099961_tabl !! n !! k

a099961_row n = a099961_tabl !! n

a099961_tabl = map snd $ iterate f (0, [1]) where

   f (s, xs) = (s+1, if s `mod` 3 == 1 then zs ++ [last zs] else zs)

     where zs = scanl1 (+) (reverse xs)

-- Reinhard Zumkeller, Dec 28 2011

CROSSREFS

First column (and row sums) gives A099962. Cf. A099963, A099967.

If an extra term is added to /every/ row we get A008282. Cf. A099959.

Sequence in context: A108221 A169682 A082524 * A286107 A285735 A038810

Adjacent sequences:  A099958 A099959 A099960 * A099962 A099963 A099964

KEYWORD

nonn,tabf,nice,easy

AUTHOR

N. J. A. Sloane, Nov 13 2004, following a suggestion made by Douglas G. Rogers, Mar 10 2003

EXTENSIONS

More terms from Emeric Deutsch, Nov 16 2004

STATUS

approved

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Last modified October 18 08:08 EDT 2019. Contains 328146 sequences. (Running on oeis4.)