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A322340 Number of compositions (ordered partitions) of n into square pyramidal numbers (A000330). 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 29 01:41 EST 2023. Contains 359905 sequences. (Running on oeis4.)