A362311 Triangle read by rows (row length 2*n+1). Row n lists the integer solutions for x in the equation x - 2^n = x/y (x and y are integers).
2, 1, 3, 4, 2, 3, 5, 6, 8, 4, 6, 7, 9, 10, 12, 16, 8, 12, 14, 15, 17, 18, 20, 24, 32, 16, 24, 28, 30, 31, 33, 34, 36, 40, 48, 64, 32, 48, 56, 60, 62, 63, 65, 66, 68, 72, 80, 96, 128, 64, 96, 112, 120, 124, 126, 127, 129, 130, 132, 136, 144, 160, 192, 256, 128, 192, 224, 240, 248, 252, 254, 255
Offset: 0
Examples
Triangle begins:
k=0 1 2 3 4 5 6 7 8
n=0: 2
n=1: 1, 3, 4
n=2: 2, 3, 5, 6, 8
n=3: 4, 6, 7, 9,10,12,16
n=4: 8,12,14,15,17,18,20,24,32
...
Corresponding values for y in the equation:
k=0 1 2 3 4 5 6 7 8
n=0: 2
n=1: -1, 3, 2
n=2: -1,-3, 5, 3, 2
n=3: -1,-3,-7, 9, 5,3,2
n=4: -1,-3,-7,-15,17,9,5,3,2
...
Programs
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MATLAB
function a = A362311( max_row ) r = 2; a = []; for n = 1:max_row a = [a r]; r = [2*r(1:n-1) 2^n-1 2^n+1 2*r(end-n+1:end)]; end end
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PARI
T(n,k) = if(k >= n, 2^n + 2^(k-n), 2^n - 2^(n-k-1));
Formula
T(n, k) = 2^n - 2^(n-k-1), if k < n.
T(n, k) = 2^n + 2^(k-n), if k >= n.
T(n, 0..n-2) = 2*T(n-1, 0..n-2), for n > 1.
T(n, n-1) = 2^n - 1, for n > 0.
T(n, n) = 2^n + 1, for n > 0.
T(n, n+1..2*n) = 2*T(n-1, n-1..2*(n-1)), for n > 0.