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$s_0(2k)=2\sum_{i=1}^k s_0(i)-s_0(k)$
$s_0(2k+1)=2\sum_{i=1}^k s_0(i)$

$s_0(2k)=2s_1(k)-(s_1(k)-s_1(k-1))=s_1(k)+s_1(k-1)$
$s_0(2k+1)=2s_1(k)$

$s_1(2k)-s_1(2k-1)=s_1(k)+s_1(k-1)$
$s_1(2k+1)-s_1(2k)=2s_1(k)$

$$

$s_1(2k)=$