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).

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

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, A277192, A277193.

Programs

Scheme

(define (A277194 n) (add A072401 (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

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

Other identities.

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

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