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A277192 Number of integers k in range [n^2, ((n+1)^2)-1] for which the least number of squares that add up to k (A002828) is even.

%I A277192 #6 Oct 05 2016 10:19:21
%S A277192 1,1,3,3,4,6,6,8,8,9,11,10,13,12,13,16,15,16,17,19,17,22,20,21,23,24,
%T A277192 23,25,26,26,28,30,28,30,31,31,31,34,34,35,35,37,37,40,38,41,42,40,44,
%U A277192 43,44,45,44,46,45,50,50,49,48,54,53,52,52,57,55,56,57,58,58,60,60,58,65,61,64,66,64,65,66,68,69,68,70,69
%N A277192 Number of integers k in range [n^2, ((n+1)^2)-1] for which the least number of squares that add up to k (A002828) is even.
%H A277192 Antti Karttunen, <a href="/A277192/b277192.txt">Table of n, a(n) for n = 0..512</a>
%F A277192 a(n) = Sum_{i=n^2 .. ((n+1)^2)-1} (1-A000035(A002828(i))).
%F A277192 For all n >= 0, A277191(n) + a(n) = 2n+1.
%F A277192 For n >= 1, a(n) = A077773(n) + A277194(n).
%o A277192 (Scheme)
%o A277192 (define (A277192 n) (add (lambda (i) (- 1 (A000035 (A002828 i)))) (A000290 n) (+ -1 (A000290 (+ 1 n)))))
%o A277192 ;; Implements sum_{i=lowlim..uplim} intfun(i)
%o A277192 (define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (1+ i) (+ res (intfun i)))))))
%Y A277192 Cf. A000035, A000290, A002828, A077773, A277191, A277194.
%K A277192 nonn
%O A277192 0,3
%A A277192 _Antti Karttunen_, Oct 04 2016