A277194 - OEIS

%I #7 Oct 05 2016 10:19:39

%S 0,0,1,1,1,2,2,3,2,3,4,4,4,4,5,6,5,5,6,7,6,8,8,8,8,8,8,10,9,10,11,11,

%T 10,11,11,12,11,13,14,13,13,13,15,15,15,15,16,16,15,17,17,17,17,17,19,

%U 19,18,19,19,21,20,21,21,22,21,21,22,23,22,23,23,25,23,24,26,25,26,26,26,27,26,27,27,28,29,28,29,30,29,30,30,31

%N Number of integers k in range [n^2, ((n+1)^2)-1] for which 4 = the least number of squares that add up to k (A002828).

%H Antti Karttunen, <a href="/A277194/b277194.txt">Table of n, a(n) for n = 0..512</a>

%F a(n) = Sum_{i=n^2 .. ((n+1)^2)-1} A072401(i).

%F Other identities.

%F For n >= 0, 1 + A077773(n) + A277193(n) + a(n) = 2n+1.

%F For n >= 1, A277192(n) = A077773(n) + a(n).

%o (Scheme)

%o (define (A277194 n) (add A072401 (A000290 n) (+ -1 (A000290 (+ 1 n)))))

%o ;; Implements sum_{i=lowlim..uplim} intfun(i)

%o (define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (1+ i) (+ res (intfun i)))))))

%Y Cf. A000290, A002828, A010052, A072401, A077773, A229062, A277192, A277193.

%K nonn

%O 0,6

%A _Antti Karttunen_, Oct 04 2016