|
|
A049986
|
|
a(n) is the number of arithmetic progressions of 4 or more positive integers, strictly increasing with sum n.
|
|
17
|
|
|
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 2, 1, 2, 0, 1, 2, 2, 1, 3, 0, 4, 0, 2, 1, 3, 4, 4, 0, 3, 1, 6, 0, 5, 0, 4, 6, 4, 0, 4, 2, 8, 2, 5, 0, 6, 6, 6, 2, 5, 0, 11, 0, 5, 5, 6, 7, 8, 0, 6, 2, 15, 0, 9, 0, 6, 10, 7, 4, 9, 0, 14, 5, 7, 0, 12, 9, 7, 3
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,20
|
|
LINKS
|
|
|
FORMULA
|
G.f.: Sum_{k >= 4} x^t(k)/(x^t(k) - x^t(k-1) - x^k + 1) = Sum_{k >= 4} x^t(k)/(1 - x^k)*(1 - x^t(k-1))), where t(k) = k*(k+1)/2 = A000217(k) is the k-th triangular number [Graeme McRae]. - Petros Hadjicostas, Sep 29 2019
|
|
PROG
|
(PARI)
|
|
CROSSREFS
|
Cf. A014405, A014406, A049980, A049981, A049982, A049983, A049987 (partial sums), A049988, A049989, A049990, A049991, A049994, A127938, A321014.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|