login
A322799
Number of compositions (ordered partitions) of n into heptagonal numbers (A000566).
7
1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 10, 13, 17, 22, 29, 37, 46, 57, 71, 89, 112, 143, 183, 233, 295, 372, 468, 588, 741, 937, 1188, 1506, 1908, 2414, 3049, 3848, 4857, 6136, 7757, 9812, 12414, 15702, 19852, 25089, 31703, 40061, 50631, 64004, 80923, 102318
OFFSET
0,8
FORMULA
G.f.: 1/(1 - Sum_{k>=1} x^(k*(5*k-3)/2)).
MAPLE
h:= proc(n) option remember; `if`(n<1, 0, (t->
`if`(t*(5*t-3)/2>n, t-1, t))(1+h(n-1)))
end:
a:= proc(n) option remember; `if`(n=0, 1,
add(a(n-i*(5*i-3)/2), i=1..h(n)))
end:
seq(a(n), n=0..60); # Alois P. Heinz, Dec 28 2018
MATHEMATICA
nmax = 53; CoefficientList[Series[1/(1 - Sum[x^(k (5 k - 3)/2), {k, 1, nmax}]), {x, 0, nmax}], x]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 26 2018
STATUS
approved