

A241290


The integervalued quartic beginning: 0, 9, 0, 9, 7.


1



0, 9, 0, 9, 7, 100, 471, 1330, 2966, 5733, 10050, 16401, 25335, 37466, 53473, 74100, 100156, 132515, 172116, 219963, 277125, 344736, 423995, 516166, 622578, 744625, 883766, 1041525, 1219491, 1419318, 1642725, 1891496, 2167480
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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 integervalued 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 integervalued polynomials.


LINKS

Table of n, a(n) for n=0..32.
Wikipedia, Integervalued 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^399*x^2+45*x9) / (x1)^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 *)


PROG

(Sage) a(n) = (65/24)*n^4 + (89/4)*n^3  (1363/24)*n^2 + (185/4)*n


CROSSREFS

Sequence in context: A237193 A132268 A252851 * A201298 A029687 A187426
Adjacent sequences: A241287 A241288 A241289 * A241291 A241292 A241293


KEYWORD

easy,sign


AUTHOR

Aaron J. Mansheim, Apr 18 2014


STATUS

approved



