A322340 Number of compositions (ordered partitions) of n into square pyramidal numbers (A000330).

1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 8, 11, 15, 20, 27, 36, 48, 64, 85, 114, 153, 205, 274, 365, 487, 651, 871, 1165, 1557, 2080, 2780, 3716, 4967, 6639, 8873, 11860, 15853, 21189, 28320, 37850, 50589, 67618, 90379, 120799, 161456, 215797, 288430, 385512, 515269, 688699

Offset: 0

Author

Ilya Gutkovskiy, Dec 26 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..7939
• Eric Weisstein's World of Mathematics, Square Pyramidal Number
• Index entries for sequences related to compositions

Crossrefs

Cf. A000330, A006456, A279220, A282582, A298246.

Programs

Maple

h:= proc(n) option remember; `if`(n<1, 0, (t->
      `if`(t*(t+1)*(2*t+1)/6>n, t-1, t))(1+h(n-1)))
    end:
a:= proc(n) option remember; `if`(n=0, 1,
      add(a(n-i*(i+1)*(2*i+1)/6), i=1..h(n)))
    end:
seq(a(n), n=0..60);  # Alois P. Heinz, Dec 28 2018

Mathematica

nmax = 49; CoefficientList[Series[1/(1 - Sum[x^(k (k + 1) (2 k + 1)/6), {k, 1, nmax}]), {x, 0, nmax}], x]

Formula

G.f.: 1/(1 - Sum_{k>=1} x^(k*(k+1)*(2*k+1)/6)).