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A099964 Triangle read by rows: The n-th row is constructed by forming the partial sums of the previous row, reading from the right and if n is a triangular number repeating the final term. 4
1, 1, 1, 1, 2, 2, 3, 3, 3, 6, 8, 8, 14, 17, 17, 31, 39, 39, 39, 78, 109, 126, 126, 235, 313, 352, 352, 665, 900, 1026, 1026, 1926, 2591, 2943, 2943, 2943, 5886, 8477, 10403, 11429, 11429, 21832, 30309, 36195, 39138, 39138, 75333, 105642, 127474, 138903 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

...

LINKS

Reinhard Zumkeller, Rows n = 0..500 of triangle, flattened

EXAMPLE

Triangle begins

     1;

     1,    1;

     1,    2,

     2,    3,    3;

     3,    6,    8,

     8,   14,   17,

    17,   31,   39,   39;

    39,   78,  109,  126,

   126,  235,  313,  352,

   352,  665,  900, 1026,

  1026, 1926, 2591, 2943, 2943;

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: tr:={seq(n*(n+1)/2, n=1..30)}: R[0]:=vector(1, 1): for n from 1 to 15 do if member(n, tr)=false then R[n]:=ps(rev(R[n-1])) else R[n]:=pss(rev(R[n-1])) fi od: for n from 0 to 15 do evalm(R[n]) od; # Emeric Deutsch, Nov 16 2004

MATHEMATICA

triQ[n_] := Reduce[ n == k(k+1)/2, k, Integers] =!= False; row[0] = {1}; row[1] = {1, 1}; row[n_] := row[n] = (ro = Accumulate[ Reverse[ row[n-1]]]; If[triQ[n], Append[ ro, Last[ro] ], ro]); Flatten[ Table[ row[n], {n, 0, 13}]](* Jean-Fran├žois Alcover, Nov 24 2011 *)

PROG

(Haskell)

a099964 n k = a099964_tabf !! n !! k

a099964_row n = a099964_tabf !! n

a099964_tabf = scanl f [1] $ tail a010054_list where

   f row t = if t == 1 then row' ++ [last row'] else row'

           where row' = scanl1 (+) $ reverse row

-- Reinhard Zumkeller, May 02 2012

CROSSREFS

First column (and row sums) gives A099965. Cf. A099966, A099968.

If an extra term is added to /every/ row we get A008282. Cf. A099959, A099961.

Cf. A010054.

Sequence in context: A115733 A025496 A099959 * A094440 A093736 A257481

Adjacent sequences:  A099961 A099962 A099963 * A099965 A099966 A099967

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 June 25 09:48 EDT 2019. Contains 324347 sequences. (Running on oeis4.)