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

0,6

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

Formula

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

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]

Crossrefs

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

Sequence in context: A003520 A101915 A295073 * A282504 A022468 A257664

Adjacent sequences: A322337 A322338 A322339 * A322341 A322342 A322343

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 26 2018

Status

approved