A261229 a(n) = number of steps to reach (n^3)-1 when starting from k = ((n+1)^3)-1 and repeatedly applying the map that replaces k with k - A055401(k), where A055401(k) = the number of positive cubes needed to sum to k using the greedy algorithm.

1, 3, 6, 9, 14, 19, 25, 31, 38, 44, 54, 62, 71, 81, 91, 103, 115, 129, 142, 157, 172, 187, 203, 221, 238, 256, 274, 294, 313, 335, 357, 378, 400, 424, 449, 473, 499, 525, 552, 579, 609, 637, 666, 698, 729, 760, 792, 827, 860, 895, 929, 967, 1002, 1039, 1077, 1117, 1155, 1195, 1235, 1278, 1318, 1361, 1404, 1448, 1492, 1538, 1583, 1631, 1677, 1725

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..512

Formula

a(n) = A261226(((n+1)^3)-1) - A261226((n^3)-1). [The definition.]

Equally, for all n >= 1:

a(n) = A261226((n+1)^3) - A261226(n^3).

a(n) = A261227(n+1) - A261227(n).

a(n) = A261228(n+1) - A261228(n).

Prog

(Scheme, three variants, the first one utilizing memoization-macro definec)
(definec (A261229 n) (let ((end (- (A000578 n) 1))) (let loop ((k (- (A000578 (+ 1 n)) 1)) (s 0)) (if (= k end) s (loop (A261225 k) (+ 1 s))))))
(define (A261229 n) (- (A261228 (+ 1 n)) (A261228 n)))
(define (A261229 n) (- (A261226 (A000578 (+ 1 n))) (A261226 (A000578 n))))

Crossrefs

First differences of both A261227 and A261228.

Cf. A000578, A055401, A261225, A261226.

Cf. also A261224.

Sequence in context: A134031 A228172 A130473 * A184015 A225282 A242771

Adjacent sequences: A261226 A261227 A261228 * A261230 A261231 A261232

Keyword

nonn

Author

Antti Karttunen, Aug 16 2015

Status

approved