login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A282173 Expansion of (Sum_{k>=0} x^(k*(k+1)*(2*k+1)/6))^6. 4
1, 6, 15, 20, 15, 12, 31, 60, 60, 30, 21, 60, 90, 60, 21, 50, 120, 120, 50, 36, 135, 210, 135, 30, 60, 186, 186, 60, 15, 120, 217, 150, 75, 120, 240, 246, 180, 180, 210, 216, 150, 180, 200, 180, 150, 200, 300, 240, 165, 180, 390, 390, 180, 60, 180, 372, 225, 110, 135, 330, 351, 270, 300, 360, 435, 300, 375, 360, 300, 210 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Number of ways to write n as an ordered sum of 6 square pyramidal numbers (A000330).
Conjecture: a(n) > 0 for all n.
Extended conjecture: every number is the sum of at most 6 square pyramidal numbers.
Generalized conjecture: every number is the sum of at most k+2 k-gonal pyramidal numbers (except k = 5). - Ilya Gutkovskiy, Feb 10 2017
LINKS
Eric Weisstein's World of Mathematics, Square Pyramidal Number
FORMULA
G.f.: (Sum_{k>=0} x^(k*(k+1)*(2*k+1)/6))^6.
EXAMPLE
a(5) = 12 because we have:
[5, 0, 0, 0, 0, 0]
[0, 5, 0, 0, 0, 0]
[0, 0, 5, 0, 0, 0]
[0, 0, 0, 5, 0, 0]
[0, 0, 0, 0, 5, 0]
[0, 0, 0, 0, 0, 5]
[1, 1, 1, 1, 1, 0]
[1, 1, 1, 1, 0, 1]
[1, 1, 1, 0, 1, 1]
[1, 1, 0, 1, 1, 1]
[1, 0, 1, 1, 1, 1]
[0, 1, 1, 1, 1, 1]
MATHEMATICA
nmax = 69; CoefficientList[Series[(Sum[x^(k (k + 1) (2 k + 1)/6), {k, 0, nmax}])^6, {x, 0, nmax}], x]
CROSSREFS
Sequence in context: A131892 A291381 A280719 * A328226 A045848 A335268
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 07 2017
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 07:30 EDT 2024. Contains 371235 sequences. (Running on oeis4.)