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

1,2

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

Table of n, a(n) for n=1..51.

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

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.

Sequence in context: A161339 A023562 A194207 * A194176 A186494 A371702

Adjacent sequences: A236535 A236536 A236537 * A236539 A236540 A236541

Keyword

nonn,tabl,easy

Author

Fedor Igumnov, Jan 28 2014

Extensions

More terms from Bruno Berselli, Jan 28 2014

Status

approved