Poor man's nth-child mixin for LT IE9. It supports single (X), repeating (Xn), repeating starting from an index (Xn+Y / Xn-Y) and odd & even. View a live demo here: http://codepen.io/stowball/pen/GxlIc

nth-child-examples.scss

.selected {
	background: #000;
	color: #fff;
}

.even > li:first-child {
	@include nth-child(even, 'li') {
		@extend .selected;
	}
}

.odd > li:first-child {
	@include nth-child(odd, 'li') {
		@extend .selected;
	}
}

.x3n > li:first-child {
	@include nth-child(3n, 'li') {
		@extend .selected;
	}
}

.x3n2 > li:first-child {
	@include nth-child((3n, 2), 'li') {
		@extend .selected;
	}
}

.x3n-2 > li:first-child {
	@include nth-child((3n, -2), 'li') {
		@extend .selected;
	}
}

.x1n4 > li {
	@include nth-child((1n, 4), 'li') {
		@extend .selected;
	}
}

.x5 > li:first-child {
	@include nth-child(5, 'li') {
		@extend .selected;
	}
}

nth-child-mixin.scss

@function strip-units($number) {
	@return $number / ($number * 0 + 1);
}

@mixin nth-child($an: 2n, $sibling: '*', $count: 15) {
	$index: '';
	$n: false;
	$selector: '';
	$modifier: 0;
	
	@if (type-of($an) == list) {
		$index: nth($an, 1);
		$modifier: nth($an, 2);
	}
	@else {
		$index: $an;
	}
	
	@if ($index == 'even' or $index == even) {
		$index: 2n;
	}
	
	@if ($index == 'odd' or $index == odd) {
		$index: 2n;
		$modifier: 1;
	}
	
	@if (unit($index) == 'n') {
		$index: strip-units($index);
		$n: true;
	}
	
	@if ($modifier < 0) {
		@if (abs($modifier) > $index){
			$modifier: -(abs($modifier) % floor($index));
		}
		$modifier: $modifier + floor($index);
	}
	
	@if ($index > 0) {	
		@if ($n == false) {
			$count: 1;
		}
		
		@if ($index == 1) {
			$selector: '&:first-child';
		}
		
		@if ($modifier > 1) {
			@for $j from 0 to $modifier - 1 {
				$selector: $selector + '+ ' + $sibling;
			}
			$selector: $selector + ',';
		}
		
		@for $i from 1 to $count + 1 {
			@if ($i > 1) {
				$selector: $selector + ', ';
			}
			@for $x from (1 - $modifier) to $index * $i {
				$selector: $selector + '+ ' + $sibling;
			}
		}
	}
	
	@if ($index > 0) {
		@if ($modifier == 1) {
			@content;
		}
		
		#{$selector} {
			@content;
		}
	}
}

nth-child-syntax.scss

nth-child($an: 2n, $sibling: '*', $count: 15)

$an - the counting method, eg: 2n, 3n, odd - default is 2n
$an can also be a list, with the 2nd parameter being the modifier, eg: 2 for ($an+2) or -3 for ($an-3)
$sibling - the sibling element selector, eg: 'li', 'div' - default is '*'
$count - how many sibling selectors to support, eg: 10, 20 - default is 15