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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.

%I A261229 #8 Mar 30 2017 21:54:43
%S A261229 1,3,6,9,14,19,25,31,38,44,54,62,71,81,91,103,115,129,142,157,172,187,
%T A261229 203,221,238,256,274,294,313,335,357,378,400,424,449,473,499,525,552,
%U A261229 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
%N 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.
%H A261229 Antti Karttunen, <a href="/A261229/b261229.txt">Table of n, a(n) for n = 1..512</a>
%F A261229 a(n) = A261226(((n+1)^3)-1) - A261226((n^3)-1). [The definition.]
%F A261229 Equally, for all n >= 1:
%F A261229 a(n) = A261226((n+1)^3) - A261226(n^3).
%F A261229 a(n) = A261227(n+1) - A261227(n).
%F A261229 a(n) = A261228(n+1) - A261228(n).
%o A261229 (Scheme, three variants, the first one utilizing memoization-macro definec)
%o A261229 (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))))))
%o A261229 (define (A261229 n) (- (A261228 (+ 1 n)) (A261228 n)))
%o A261229 (define (A261229 n) (- (A261226 (A000578 (+ 1 n))) (A261226 (A000578 n))))
%Y A261229 First differences of both A261227 and A261228.
%Y A261229 Cf. A000578, A055401, A261225, A261226.
%Y A261229 Cf. also A261224.
%K A261229 nonn
%O A261229 1,2
%A A261229 _Antti Karttunen_, Aug 16 2015