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
Fedor Igumnov, T(n,k) for n = 1..26
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
KEYWORD
AUTHOR
Fedor Igumnov, Jan 28 2014
EXTENSIONS
More terms from Bruno Berselli, Jan 28 2014
STATUS
approved