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Search: id:A099959
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| A099959 |
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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 other row repeating the final term. |
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+0
5
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| 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, 155, 310, 448, 552, 608, 608, 1160, 1608, 1918, 2073, 2073, 2073, 4146, 6064, 7672, 8832, 9440, 9440, 18272, 25944, 32008, 36154, 38227, 38227, 38227, 76454, 112608
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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...
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EXAMPLE
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Triangle begins
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
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MAPLE
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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 (Deutsch)
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CROSSREFS
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First column (and row sums) gives A099960.
If an extra term is added to /every/ row we get A008282. Cf. A099961.
Sequence in context: A080968 A115733 A025496 this_sequence A099964 A094440 A093736
Adjacent sequences: A099956 A099957 A099958 this_sequence A099960 A099961 A099962
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KEYWORD
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nonn,tabf,nice,easy
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AUTHOR
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njas, Nov 13 2004, following a suggestion made by Douglas G. Rogers, Mar 10, 2003
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 16 2004
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