A284000 a(n) = a(a(n-A002828(n))) + a(n-a(n-A002828(n))) with a(1) = a(2) = a(3) = 1, where A002828(n) = the least number of squares that add up to n.

1, 1, 1, 2, 3, 4, 5, 4, 5, 6, 7, 8, 9, 10, 9, 10, 9, 10, 11, 12, 13, 14, 15, 16, 15, 16, 17, 18, 17, 18, 19, 20, 19, 22, 21, 22, 23, 22, 23, 24, 25, 26, 27, 26, 27, 28, 29, 30, 29, 30, 31, 32, 33, 34, 35, 34, 37, 38, 37, 38, 39, 38, 39, 38, 39, 40, 39, 42, 41, 42

Offset

1,4

Comments

Does a(n)/n converge to some value near 0.6 ? See for example: a(10) = 6, a(100) = 62, a(1000) = 604, a(10000) = 6050, a(100000) = 60414.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10001

Formula

For n <= 3 a(n) = 1, else a(n) = a(a(A255131(n))) + a(n-a(A255131(n))).

Prog

(Scheme, with memoization-macro definec)
(definec (A284000 n) (if (<= n 3) 1 (+ (A284000 (A284000 (- n (A002828 n)))) (A284000 (- n (A284000 (- n (A002828 n))))))))

Crossrefs

Cf. A002828, A004001, A255131, A284006, A284007.

Sequence in context: A325631 A276073 A341311 * A309293 A244904 A338885

Adjacent sequences: A283997 A283998 A283999 * A284001 A284002 A284003

Keyword

nonn

Author

Antti Karttunen, Mar 23 2017

Status

approved