|
|
A014798
|
|
Squares of even square pyramidal numbers.
|
|
2
|
|
|
196, 900, 19600, 41616, 256036, 422500, 1537600, 2238016, 6100900, 8236900, 18696976, 24010000, 48024900, 59505796, 108493056, 130873600, 222308100, 262634436, 421891600, 490179600, 752624356, 862596900, 1275918400, 1445824576, 2072616676, 2326132900, 3246720400
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
LINKS
|
Index entries for linear recurrences with constant coefficients, signature (1,6,-6,-15,15,20,-20,-15,15,6,-6,-1,1).
|
|
FORMULA
|
G.f.: -4*(49*x^10 +176*x^9 +4381*x^8 +4448*x^7 +26290*x^6 +11232*x^5 +26290*x^4 +4448*x^3 +4381*x^2 +176*x +49)/((x -1)^7*(x +1)^6). - Colin Barker, Nov 16 2012
Sum_{n>=0} 1/a(n) = (165/4 + 18*sqrt(2))*Pi^2 + 54*Pi - 828. - Amiram Eldar, Mar 07 2022
|
|
MATHEMATICA
|
CoefficientList[Series[- 4 (49 x^10 + 176 x^9 + 4381 x^8 + 4448 x^7 + 26290 x^6 + 11232 x^5 + 26290 x^4 + 4448 x^3 + 4381 x^2 + 176 x + 49)/((x - 1)^7 (x + 1)^6), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 15 2013 *)
Select[Table[n*(n + 1)*(2*n + 1)/6, {n, 1, 70}], EvenQ]^2 (* Amiram Eldar, Mar 07 2022 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|