cp's OEIS Frontend

A277194 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).

%I A277194 #7 Oct 05 2016 10:19:39
%S A277194 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 A277194 10,11,11,12,11,13,14,13,13,13,15,15,15,15,16,16,15,17,17,17,17,17,19,
%U A277194 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 A277194 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 A277194 Antti Karttunen, <a href="/A277194/b277194.txt">Table of n, a(n) for n = 0..512</a>
%F A277194 a(n) = Sum_{i=n^2 .. ((n+1)^2)-1} A072401(i).
%F A277194 Other identities.
%F A277194 For n >= 0, 1 + A077773(n) + A277193(n) + a(n) = 2n+1.
%F A277194 For n >= 1, A277192(n) = A077773(n) + a(n).
%o A277194 (Scheme)
%o A277194 (define (A277194 n) (add A072401 (A000290 n) (+ -1 (A000290 (+ 1 n)))))
%o A277194 ;; Implements sum_{i=lowlim..uplim} intfun(i)
%o A277194 (define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (1+ i) (+ res (intfun i)))))))
%Y A277194 Cf. A000290, A002828, A010052, A072401, A077773, A229062, A277192, A277193.
%K A277194 nonn
%O A277194 0,6
%A A277194 _Antti Karttunen_, Oct 04 2016