|
|
A071910
|
|
a(n) = t(n)*t(n+1)*t(n+2), where t() are the triangular numbers.
|
|
1
|
|
|
0, 18, 180, 900, 3150, 8820, 21168, 45360, 89100, 163350, 283140, 468468, 745290, 1146600, 1713600, 2496960, 3558168, 4970970, 6822900, 9216900, 12273030, 16130268, 20948400, 26910000, 34222500, 43120350, 53867268, 66758580, 82123650, 100328400, 121777920
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
a(n) is also the number of three-dimensional cage assemblies such that the assembly is not a cube. See also A052149 for the two-dimensional version and to A059827 for the non-exclusive version. - Alejandro Rodriguez, Oct 20 2020
|
|
LINKS
|
|
|
FORMULA
|
a(n) = ((n+1)*(n+2))^3/8 - Sum_{i=1..n+1} i^3. - Jon Perry, Feb 13 2004
|
|
PROG
|
(PARI) t(n) = n*(n+1)/2;
|
|
CROSSREFS
|
Cf. A006542, (first differences of a(n) /18) A006414, (second differences of a(n) /18) A006322, (third differences of a(n) /18) A004068, (fourth differences of a(n) /18) A005891, (fifth differences of a(n) /18) A008706.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|