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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
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.
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
KEYWORD
nonn,tabl,easy
AUTHOR
Fedor Igumnov, Jan 28 2014
EXTENSIONS
More terms from Bruno Berselli, Jan 28 2014
STATUS
approved