OFFSET
1,9
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..12580 (first 1000 terms from Fausto A. C. Cariboni)
Sadek Bouroubi and Nesrine Benyahia Tani, Integer partitions into arithmetic progressions, Rostok. Math. Kolloq. 64 (2009), 11-16.
Sadek Bouroubi and Nesrine Benyahia Tani, Integer partitions into arithmetic progressions with an odd common difference, Integers 9(1) (2009), 77-81.
Graeme McRae, Counting arithmetic sequences whose sum is n.
Graeme McRae, Counting arithmetic sequences whose sum is n [Cached copy]
Augustine O. Munagi, Combinatorics of integer partitions in arithmetic progression, Integers 10(1) (2010), 73-82.
Augustine O. Munagi and Temba Shonhiwa, On the partitions of a number into arithmetic progressions, Journal of Integer Sequences 11 (2008), Article 08.5.4.
A. N. Pacheco Pulido, Extensiones lineales de un poset y composiciones de números multipartitos, Maestría thesis, Universidad Nacional de Colombia, 2012.
Wikipedia, Arithmetic progression.
FORMULA
G.f.: Sum_{k >= 3} x^t(k)/(x^t(k) - x^t(k-1) - x^k + 1) = Sum_{k >= 3} 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
EXAMPLE
E.g., 15 = 1+2+3+4+5 = 1+5+9 = 2+5+8 = 3+5+7 = 4+5+6.
PROG
(PARI) a(n)= t=0; st=0; forstep(s=(n-3)\3, 1, -1, st++; for(c=1, st, m=3; w=m*(s+c); while(w<n, w=w+s+m*c; m++); if(w==n, t++))); t \\ Rick L. Shepherd, Aug 30 2006
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved