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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.

%I A236538 #43 Mar 28 2024 21:56:50
%S A236538 1,3,5,8,12,16,20,28,36,44,48,64,80,96,112,112,144,176,208,240,272,
%T A236538 256,320,384,448,512,576,640,576,704,832,960,1088,1216,1344,1472,1280,
%U A236538 1536,1792,2048,2304,2560,2816,3072,3328,2816,3328,3840,4352,4864,5376
%N A236538 Triangle read by rows: T(n,k) = (n+1)*2^(n-2)+(k-1)*2^(n-1) for 1 <= k <= n.
%C A236538 1, 9, 45, 161, 497, 1409, ... is the sequence of perimeters (sum of border elements) of the triangle.
%C A236538 1, 5, 80, 3520, 394240, 107233280, 68629299200, ... is the sequence of determinants of the triangle.
%C A236538 Only the first three terms are odd.
%H A236538 Fedor Igumnov, <a href="/A236538/a236538.txt">T(n,k) for n = 1..26</a>
%F A236538 T(n,k) = T(n-1,k) + T(n-1,k+1).
%F A236538 Sum_{k=1..n} T(n,k) = n^2*2^(n-1) = A014477(n-1).
%e A236538 Triangle begins:
%e A236538 ================================================
%e A236538 \k |    1     2     3     4     5     6     7
%e A236538 n\ |
%e A236538 ================================================
%e A236538 1  |    1;
%e A236538 2  |    3,    5;
%e A236538 3  |    8,   12,   16;
%e A236538 4  |   20,   28,   36,   44;
%e A236538 5  |   48,   64,   80,   96,  112;
%e A236538 6  |  112,  144,  176,  208,  240,  272;
%e A236538 7  |  256,  320,  384,  448,  512,  576,  640;
%e A236538 ...
%t A236538 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 *)
%o A236538 (C) int a(int n, int k) {return (n+1)*pow(2,n-2)+(k-1)*pow(2,n-1);}
%o A236538 (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
%Y A236538 Cf. A001792 (column 1), A053220 (right border). Also:
%Y A236538 A014477, row sums;
%Y A236538 A036826, partial sums;
%Y A236538 A058962, central elements in odd rows;
%Y A236538 A045623, second column;
%Y A236538 A045891, third column;
%Y A236538 A034007, fourth column;
%Y A236538 A167667, subdiagonal;
%Y A236538 A130129, second subdiagonal.
%K A236538 nonn,tabl,easy
%O A236538 1,2
%A A236538 _Fedor Igumnov_, Jan 28 2014
%E A236538 More terms from _Bruno Berselli_, Jan 28 2014