Sequences And Series

Let \(\alpha=1^2+4^2+8^2+13^2+19^2+26^2+\ldots\) upto 10 terms and \(\beta=\sum_\limits{n=1}^{10} n^4\). If \(4 \alpha-\beta=55 k+40\), then \(\mathrm{k}\) is equal to __________.