OFFSET
0,2
COMMENTS
At time of submission, <0, 9, 0, 9, 7> was the "smallest uninteresting number", in the sense that it was the least sequence of five decimal digits that was not retrieved when searching the encyclopedia (primarily offline using the sagemath interface "SloaneEncyclopedia").
The initial sequence <0, 9, 0, 9, 7> happens to define an integer-valued quartic:
a(n) = -65 p_4(n) + 36 p_3(n) - 18 p_2(n) + 9 p_1(n), n >= 0,
where the polynomials p_k(t) = binomial(t, k) are a basis for integer-valued polynomials.
LINKS
Wikipedia, Integer-valued polynomial
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = -(65/24)*n^4 + (89/4)*n^3 - (1363/24)*n^2 + (185/4)*n.
G.f.: x*(128*x^3-99*x^2+45*x-9) / (x-1)^5. - Colin Barker, Apr 19 2014
MAPLE
A241290:=n->-(65/24)*n^4 + (89/4)*n^3 - (1363/24)*n^2 + (185/4)*n; seq(A241290(n), n=0..50); # Wesley Ivan Hurt, Apr 18 2014
MATHEMATICA
Table[-(65/24)*n^4 + (89/4)*n^3 - (1363/24)*n^2 + (185/4)*n, {n, 0, 50}] (* Wesley Ivan Hurt, Apr 18 2014 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 9, 0, 9, 7}, 50] (* Harvey P. Dale, Apr 02 2023 *)
PROG
(Sage) a(n) = -(65/24)*n^4 + (89/4)*n^3 - (1363/24)*n^2 + (185/4)*n
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Aaron J. Mansheim, Apr 18 2014
STATUS
approved