|
Search: id:A099961
|
|
|
| A099961 |
|
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. |
|
+0
6
|
|
| 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; listen)
|
|
|
OFFSET
|
0,6
|
|
|
COMMENT
|
...
|
|
EXAMPLE
|
Triangle begins
1
1
1 1
1 2
2 3
3 5 5
5 10 13
13 23 28
28 51 64 64
|
|
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)
|
|
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: A045767 A108221 A082524 this_sequence A038810 A086609 A035031
Adjacent sequences: A099958 A099959 A099960 this_sequence A099962 A099963 A099964
|
|
KEYWORD
|
nonn,tabf,nice,easy
|
|
AUTHOR
|
njas, Nov 13 2004, following a suggestion made by Douglas G. Rogers, Mar 10, 2003
|
|
EXTENSIONS
|
More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 16 2004
|
|
|
Search completed in 0.002 seconds
|
