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 A099959 Triangle read by rows: Each row is constructed by forming the partial sums of the previous row, reading from the right and at every other row repeating the final term. 6

%I

%S 1,1,1,1,1,2,2,3,3,3,6,8,8,14,17,17,17,34,48,56,56,104,138,155,155,

%T 155,310,448,552,608,608,1160,1608,1918,2073,2073,2073,4146,6064,7672,

%U 8832,9440,9440,18272,25944,32008,36154,38227,38227,38227,76454,112608

%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 other row repeating the final term.

%C ...

%H Reinhard Zumkeller, <a href="/A099959/b099959.txt">Rows n=0..119 of triangle, flattened</a>

%e Triangle begins

%e 1;

%e 1,

%e 1, 1;

%e 1, 2,

%e 2, 3, 3;

%e 3, 6, 8,

%e 8, 14, 17, 17;

%e 17, 34, 48, 56,

%e 56, 104, 138, 155, 155;

%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 18 do if n mod 2 = 1 then R[n]:=ps(rev(R[n-1])) else R[n]:=pss(rev(R[n-1])) fi od: for n from 0 to 18 do evalm(R[n]) od; # program yields the successive rows # _Emeric Deutsch_, Nov 16 2004

%t row[0] = row[1] = {1}; row[n_?OddQ] := Accumulate[ Reverse[ row[n-1] ] ]; row[n_?EvenQ] := (r = Accumulate[ Reverse[ row[n-1] ] ]; AppendTo[r, Last[r] ]); Flatten[ Table[ row[n], {n, 0, 13}]] (* _Jean-François Alcover_, Dec 16 2011 *)

%o a099959 n k = a099959_tabl !! n !! k

%o a099959_row n = a099959_tabl !! n

%o a099959_tabl = map snd \$ iterate f (False,[1]) where

%o f (s,xs) = (not s, if s 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 A099960.

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

%K nonn,tabf,nice,easy

%O 0,6

%A _N. J. A. Sloane_, Nov 13 2004, following a suggestion made by Douglas G. Rogers, Mar 10 2003

%E More terms from _Emeric Deutsch_, Nov 16 2004

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Last modified June 16 15:17 EDT 2019. Contains 324152 sequences. (Running on oeis4.)