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Number of compositions of n, where the difference between the number of odd parts and the number of even parts is 4.

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`%I #7 May 20 2014 02:41:59
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`%S 1,0,4,6,10,36,48,126,259,456,1064,1956,3939,8112,15300,31174,60951,
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`%T 118580,236456,458172,900185,1765556,3431792,6728410,13107393,
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`%U 25538448,49856392,96966572,188914574,367741688,715053048,1391512424,2705016795,5258241032
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`%N Number of compositions of n, where the difference between the number of odd parts and the number of even parts is 4.
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`%C With offset 8 number of compositions of n, where the difference between the number of odd parts and the number of even parts is -4.
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`%H Alois P. Heinz, <a href="/A242502/b242502.txt">Table of n, a(n) for n = 4..1000</a>
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`%F Recurrence (for n>=8): (n-4)*(n+8)*(2*n-3)*(2*n-1)*(n^4 - 2*n^3 - n^2 + 2*n - 256)*a(n) = -64*(n-5)*(n-1)*(n+7)*(2*n-3)*(2*n+1)*a(n-1) + 2*(2*n-1)*(2*n^7 - n^6 + 14*n^5 - 199*n^4 - 288*n^3 + 600*n^2 - 5360*n + 2928)*a(n-2) + 2*(n-1)*(2*n-3)*(2*n+1)*(2*n^5 + n^4 - 9*n^3 + 28*n^2 - 508*n + 608)*a(n-3) - (n-4)*n*(2*n-1)*(2*n+1)*(n^4 + 2*n^3 - n^2 - 2*n - 256)*a(n-4). - _Vaclav Kotesovec_, May 20 2014
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`%Y Column k=4 of A242498.
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`%K nonn
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`%O 4,3
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`%A _Alois P. Heinz_, May 16 2014
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