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.
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
Offset: 0
Examples
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;
Links
- Reinhard Zumkeller, Rows n = 0..500 of triangle, flattened
Crossrefs
Programs
-
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 -
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 *)
Extensions
More terms from Emeric Deutsch, Nov 16 2004
Comments