|
| |
|
|
A304993
|
|
a(n) = n*(n + 1)*(7*n + 5)/6.
|
|
4
|
|
|
|
0, 4, 19, 52, 110, 200, 329, 504, 732, 1020, 1375, 1804, 2314, 2912, 3605, 4400, 5304, 6324, 7467, 8740, 10150, 11704, 13409, 15272, 17300, 19500, 21879, 24444, 27202, 30160, 33325, 36704, 40304, 44132, 48195, 52500, 57054, 61864, 66937, 72280, 77900, 83804, 89999, 96492
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
The sequence provides the sums of the triangular numbers from A000217(n) to A000217(2*n).
|
|
|
LINKS
|
|
|
|
FORMULA
|
O.g.f.: x*(4 + 3*x)/(1 - x)^4.
E.g.f.: x*(24 + 33*x + 7*x^2)*exp(x)/6.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
a(n) = Sum_{k = n..2*n} k*(k+1)/2.
|
|
|
MATHEMATICA
|
Table[n (n + 1) (7 n + 5)/6, {n, 0, 50}]
LinearRecurrence[{4, -6, 4, -1}, {0, 4, 19, 52}, 50] (* Harvey P. Dale, May 03 2023 *)
|
|
|
PROG
|
(PARI) concat(0, Vec(x*(4 + 3*x)/(1 - x)^4 + O(x^40))) \\ Colin Barker, May 25 2018
|
|
|
CROSSREFS
|
Row sums of the triangle in A141433.
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
