login
Number of positive integers that are not the sum of 3 squares and a nonnegative (2n + 1)-st power.
1

%I #17 Jan 28 2020 03:42:46

%S 0,0,17,191,1816,16541,149320,1344880,12106148,108960347,980654368,

%T 8825914594,79433288194,714899721602,6434097782077,57906880685893,

%U 521161927629204,4690457351939133,42214116174823814,379927045590000351,3419343410347321718

%N Number of positive integers that are not the sum of 3 squares and a nonnegative (2n + 1)-st power.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Legendre%27s_three-square_theorem">Legendre's three-square theorem</a>

%F a(n) = Sum_{k=2..n-1} (floor(3^(2n+1)/2^(2k+3)-7/8) + 1).

%t a[n_]:=Sum[Floor[3^(2n+1)/2^(2k+3)-7/8]+1, {k,2,n-1}];

%t Table[a[n], {n,21}]

%Y Cf. A004215, A297788, A273915, A297970, A296579, A299796.

%K nonn

%O 1,3

%A _XU Pingya_, Nov 27 2018