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%I #24 Aug 03 2021 19:05:00
%S 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,
%T 207,386,514,578,578,1092,1478,1685,1685,1685,3370,4848,5940,6518,
%U 6518,12458,17306,20676,22361,22361,43037,60343,72801,79319,79319,79319
%N 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.
%C ...
%H Reinhard Zumkeller, <a href="/A099961/b099961.txt">Rows n=0..120 of triangle, flattened</a>
%e Triangle begins
%e 1;
%e 1,
%e 1, 1;
%e 1, 2,
%e 2, 3,
%e 3, 5, 5;
%e 5, 10, 13,
%e 13, 23, 28,
%e 28, 51, 64, 64;
%p 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
%t 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-François Alcover_, Mar 13 2012 *)
%o (Haskell)
%o a099961 n k = a099961_tabl !! n !! k
%o a099961_row n = a099961_tabl !! n
%o a099961_tabl = map snd $ iterate f (0,[1]) where
%o f (s,xs) = (s+1, if s `mod` 3 == 1 then zs ++ [last zs] else zs)
%o where zs = scanl1 (+) (reverse xs)
%o -- _Reinhard Zumkeller_, Dec 28 2011
%Y First column (and row sums) gives A099962. Cf. A099963, A099967.
%Y If an extra term is added to /every/ row we get A008282. Cf. A099959.
%K nonn,tabf,nice,easy
%O 0,6
%A _N. J. A. Sloane_, Nov 13 2004
%E More terms from _Emeric Deutsch_, Nov 16 2004
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