A277193 Number of integers k in range [n^2, ((n+1)^2)-1] for which 3 = the least number of squares that add up to k (A002828).

0, 1, 1, 3, 4, 4, 6, 6, 8, 9, 9, 12, 11, 14, 15, 14, 17, 18, 19, 19, 23, 20, 24, 25, 25, 26, 29, 29, 30, 32, 32, 32, 36, 36, 37, 39, 41, 40, 42, 43, 45, 45, 47, 46, 50, 49, 50, 54, 52, 55, 56, 57, 60, 60, 63, 60, 62, 65, 68, 64, 67, 70, 72, 69, 73, 74, 75, 76, 78, 78, 80, 84, 79, 85, 84, 84, 88, 89, 90, 90, 91, 94, 94, 97, 94, 99

Offset: 0

Author

Antti Karttunen, Oct 04 2016

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..512

Crossrefs

Cf. A000290, A002828, A010052, A072401, A077773, A229062, A277194.

After the initial zero, one less than A277191.

Programs

Scheme

(define (A277193 n) (add (lambda (i) (* (- 1 (A010052 i)) (- 1 (A229062 i)) (- 1 (A072401 i)))) (A000290 n) (+ -1 (A000290 (+ 1 n)))))
;; Implements sum_{i=lowlim..uplim} intfun(i)
(define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (1+ i) (+ res (intfun i)))))))

Formula

Sum_{i=n^2 .. ((n+1)^2)-1} (1-A010052(i))*(1-A229062(i))*(1-A072401(i)).

Other identities. For all n >= 0:

1 + A077773(n) + a(n) + A277194(n) = 2n+1.

For n >= 1, a(n) = A277191(n)-1.