A236538 Triangle read by rows: T(n,k) = (n+1)*2^(n-2)+(k-1)*2^(n-1) for 1 <= k <= n.

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

Offset: 1

Author

Fedor Igumnov, Jan 28 2014

Keywords

• nonn
• tabl
• easy

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.

Examples

			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;
...
		

Links

• Fedor Igumnov, T(n,k) for n = 1..26

Crossrefs

Cf. A001792 (column 1), A053220 (right border). Also:

A014477, row sums;

A036826, partial sums;

A058962, central elements in odd rows;

A045623, second column;

A045891, third column;

A034007, fourth column;

A167667, subdiagonal;

A130129, second subdiagonal.

Programs

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

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 *)

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).

Extensions

More terms from Bruno Berselli, Jan 28 2014