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A322798
Number of compositions (ordered partitions) of n into hexagonal numbers (A000384).
7
1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 9, 12, 16, 22, 29, 37, 47, 60, 77, 101, 133, 174, 226, 292, 376, 486, 632, 823, 1072, 1394, 1808, 2342, 3036, 3939, 5116, 6648, 8636, 11211, 14548, 18875, 24493, 31795, 41283, 53604, 69594, 90338, 117251, 152184, 197540
OFFSET
0,7
FORMULA
G.f.: 1/(1 - Sum_{k>=1} x^(k*(2*k-1))).
MAPLE
h:= proc(n) option remember; `if`(n<1, 0, (t->
`if`(t*(2*t-1)>n, t-1, t))(1+h(n-1)))
end:
a:= proc(n) option remember; `if`(n=0, 1,
add(a(n-i*(2*i-1)), i=1..h(n)))
end:
seq(a(n), n=0..60); # Alois P. Heinz, Dec 28 2018
MATHEMATICA
nmax = 50; CoefficientList[Series[1/(1 - Sum[x^(k (2 k - 1)), {k, 1, nmax}]), {x, 0, nmax}], x]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 26 2018
STATUS
approved