|
|
A236538
|
|
Triangle read by rows: T(n,k) = (n+1)*2^(n-2)+(k-1)*2^(n-1) for 1 <= k <= n.
|
|
1
|
|
|
1, 3, 5, 8, 12, 16, 20, 28, 36, 44, 48, 64, 80, 96, 112, 112, 144, 176, 208, 240, 272, 256, 320, 384, 448, 512, 576, 640, 576, 704, 832, 960, 1088, 1216, 1344, 1472, 1280, 1536, 1792, 2048, 2304, 2560, 2816, 3072, 3328, 2816, 3328, 3840, 4352, 4864, 5376
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
1, 9, 45, 161, 497, 1409, ... is the sequence of perimeters (sum of border elements) of the triangle.
1, 5, 80, 3520, 394240, 107233280, 68629299200, ... is the sequence of determinants of the triangle.
Only the first three terms are odd.
|
|
LINKS
|
|
|
FORMULA
|
T(n,k) = T(n-1,k) + T(n-1,k+1).
Sum_{k=1..n} T(n,k) = n^2*2^(n-1) = A014477(n-1).
|
|
EXAMPLE
|
Triangle begins:
================================================
\k | 1 2 3 4 5 6 7
n\ |
================================================
1 | 1;
2 | 3, 5;
3 | 8, 12, 16;
4 | 20, 28, 36, 44;
5 | 48, 64, 80, 96, 112;
6 | 112, 144, 176, 208, 240, 272;
7 | 256, 320, 384, 448, 512, 576, 640;
...
|
|
MATHEMATICA
|
t[n_, k_] := (n + 1)*2^(n - 2) + (k - 1)*2^(n - 1); Table[t[n, k], {n, 10}, {k, n}] // Flatten (* Bruno Berselli, Jan 28 2014 *)
|
|
PROG
|
(C) int a(int n, int k) {return (n+1)*pow(2, n-2)+(k-1)*pow(2, n-1); }
(Magma) /* As triangle: */ [[(n+1)*2^(n-2)+(k-1)*2^(n-1): k in [1..n]]: n in [1..10]]; // Bruno Berselli, Jan 28 2014
|
|
CROSSREFS
|
A058962, central elements in odd rows;
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|