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A099961
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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.
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6
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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, 207, 386, 514, 578, 578, 1092, 1478, 1685, 1685, 1685, 3370, 4848, 5940, 6518, 6518, 12458, 17306, 20676, 22361, 22361, 43037, 60343, 72801, 79319, 79319, 79319
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| ...
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LINKS
| Reinhard Zumkeller, Rows n=0..120 of triangle, flattened
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EXAMPLE
| Triangle begins
1
1
1 1
1 2
2 3
3 5 5
5 10 13
13 23 28
28 51 64 64
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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: 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 (Deutsch)
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PROG
| (Haskell)
a099961 n k = a099961_tabl !! n !! k
a099961_row n = a099961_tabl !! n
a099961_tabl = map snd $ iterate f (0, [1]) where
f (s, xs) = (s+1, if s `mod` 3 == 1 then zs ++ [last zs] else zs)
where zs = scanl1 (+) (reverse xs)
-- Reinhard Zumkeller, Dec 28 2011
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CROSSREFS
| First column (and row sums) gives A099962. Cf. A099963, A099967.
If an extra term is added to /every/ row we get A008282. Cf. A099959.
Sequence in context: A108221 A169682 A082524 * A038810 A178503 A179254
Adjacent sequences: A099958 A099959 A099960 * A099962 A099963 A099964
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KEYWORD
| nonn,tabf,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 13 2004, following a suggestion made by Douglas G. Rogers, Mar 10, 2003
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 16 2004
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