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Given a number n, find sum of square of first n even natural numbers.
Examples:
Input : 3
Output : 56
22 + 42 + 62 = 56
Input : 8
Output : 816
22 + 42 + 62 + 82 + 102 + 122 + 142 + 162 = 816
A simple solution is to traverse through n even numbers and find the sum of square.
C++
<?php
function squareSum($n)
{
$sum = 0;
for ($i = 1; $i <= $n; $i++)
$sum += (2 * $i) * (2 * $i);
return $sum;
}
echo squareSum(8);
?>
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Javascript
<?php
function squareSum( $n)
{
return 2 * $n * ($n + 1) *
(2 * $n + 1) / 3;
}
echo squareSum(8);
?>
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Javascript
<script>
function squareSum(n)
{
let sum = 0;
for (let i = 1; i <= n; i++)
sum += (2 * i) * (2 * i);
return sum;
}
document.write(squareSum(8));
</script>
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Output :
816
Time complexity: O(1) since performing constant operations
Auxiliary Space: O(1) because constant extra space has been used
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