|
| |
|
|
A156856
|
|
a(n) = 2025*n^2 + n.
|
|
5
|
|
|
|
2026, 8102, 18228, 32404, 50630, 72906, 99232, 129608, 164034, 202510, 245036, 291612, 342238, 396914, 455640, 518416, 585242, 656118, 731044, 810020, 893046, 980122, 1071248, 1166424, 1265650, 1368926, 1476252, 1587628, 1703054, 1822530
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
The identity (32805000*n^2 + 16200*n + 1)^2 - (2025*n^2 + n)*(729000*n + 180)^2 = 1 can be written as A157081(n)^2 - a(n)*A156868(n)^2 = 1.
|
|
|
LINKS
|
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
|
|
|
FORMULA
|
From R. J. Mathar, Mar 09 2009: (Start)
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
G.f.: 2*x*(1013 + 1012*x)/(1-x)^3. (End)
E.g.f.: x*(2026 + 2025*x)*exp(x). - G. C. Greubel, Jan 28 2022
|
|
|
MATHEMATICA
|
LinearRecurrence[{3, -3, 1}, {2026, 8102, 18228}, 40]
|
|
|
PROG
|
(Magma) I:=[2026, 8102, 18228]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
(PARI) a(n)=n*(2025*n+1) \\ Charles R Greathouse IV, Dec 23 2011
(Sage) [n*(2025*n +1) for n in (1..40)] # G. C. Greubel, Jan 28 2022
|
|
|
CROSSREFS
|
Cf. A156855, A156868, A157081.
A subsequence of A031768.
Sequence in context: A250811 A350869 A031768 * A031543 A031723 A145721
Adjacent sequences: A156853 A156854 A156855 * A156857 A156858 A156859
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Vincenzo Librandi, Feb 17 2009
|
|
|
STATUS
|
approved
|
| |
|
|
