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A256264
Partial sums of A256263.
8
0, 1, 2, 5, 6, 9, 14, 21, 22, 25, 30, 37, 42, 53, 70, 85, 86, 89, 94, 101, 106, 117, 134, 149, 154, 165, 182, 205, 234, 269, 310, 341, 342, 345, 350, 357, 362, 373, 390, 405, 410, 421, 438, 461, 490, 525, 566, 597, 602, 613, 630, 653, 682, 717, 758, 805, 858, 917, 982, 1053, 1130, 1213, 1302, 1365
OFFSET
0,3
COMMENTS
First differs from A255747 at a(27).
FORMULA
a(n) = (A256260(n+1) - 1)/4.
EXAMPLE
Also, written as an irregular triangle in which the row lengths are the terms of A011782, the sequence begins:
0,
1,
2, 5,
6, 9, 14, 21,
22, 25, 30, 37, 42, 53, 70, 85;
86, 89, 94, 101, 106, 117, 134, 149, 154, 165, 182, 205, 234, 269,310,341;
...
It appears that the first column gives 0 together with the terms of A047849, hence the right border gives A002450.
It appears that this triangle at least shares with the triangles from the following sequences; A151920, A255737, A255747, A256249, the positive elements of the columns k, if k is a power of 2.
From _Omar E. Pol, Jan 02 2016: (Start)
Illustration of initial terms in the fourth quadrant of the square grid:
---------------------------------------------------------------------------
n a(n) Compact diagram
---------------------------------------------------------------------------
0 0 _
1 1 |_|_ _
2 2 |_| |
3 5 |_ _|_ _ _ _
4 6 |_| | | |
5 9 |_ _| | |
6 14 |_ _ _| |
7 21 |_ _ _ _|_ _ _ _ _ _ _ _
8 22 |_| | | |_ _ | |
9 25 |_ _| | |_ | | |
10 30 |_ _ _| | | | | |
11 37 |_ _ _ _| | | | |
12 42 | | |_ _ _| | | |
13 53 | |_ _ _ _ _| | |
14 70 |_ _ _ _ _ _ _| |
15 85 |_ _ _ _ _ _ _ _|_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
16 86 |_| | | |_ _ | |_ _ _ _ _ _ | |
17 89 |_ _| | |_ | | |_ _ _ _ _ | | |
18 94 |_ _ _| | | | | |_ _ _ _ | | | |
19 101 |_ _ _ _| | | | |_ _ _ | | | | |
20 106 | | |_ _ _| | | |_ _ | | | | | |
21 117 | |_ _ _ _ _| | |_ | | | | | | |
22 134 |_ _ _ _ _ _ _| | | | | | | | | |
23 149 |_ _ _ _ _ _ _ _| | | | | | | | |
24 154 | | | | | | |_ _ _| | | | | | | |
25 165 | | | | | |_ _ _ _ _| | | | | | |
26 182 | | | | |_ _ _ _ _ _ _| | | | | |
27 205 | | | |_ _ _ _ _ _ _ _ _| | | | |
28 234 | | |_ _ _ _ _ _ _ _ _ _ _| | | |
29 269 | |_ _ _ _ _ _ _ _ _ _ _ _ _| | |
30 310 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _| |
31 341 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|
.
a(n) is also the total number of cells in the first n regions of the diagram. A256263(n) gives the number of cells in the n-th region of the diagram.
(End)
MATHEMATICA
Accumulate@Flatten@Join[{0}, NestList[Join[#, Range[Length[#] - 1]*6 - 1, {2 #[[-1]] + 1}] &, {1}, 5]] (* Ivan Neretin, Feb 14 2017 *)
KEYWORD
nonn,look
AUTHOR
Omar E. Pol, Mar 30 2015
STATUS
approved