A241290 The integer-valued quartic beginning: 0, 9, 0, 9, 7.

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

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

Table of n, a(n) for n=0..32.

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

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