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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-François 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.)