A136316 a(n) = 13 + 12*n - n^2.

13, 24, 33, 40, 45, 48, 49, 48, 45, 40, 33, 24, 13, 0, -15, -32, -51, -72, -95, -120, -147, -176, -207, -240, -275, -312, -351, -392, -435, -480, -527, -576, -627, -680, -735, -792, -851, -912, -975, -1040, -1107, -1176, -1247, -1320, -1395, -1472, -1551, -1632, -1715, -1800, -1887, -1976, -2067, -2160, -2255

Offset

0,1

References

Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 62 or 63.

Links

Table of n, a(n) for n=0..54.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

From Elmo R. Oliveira, Nov 18 2024: (Start)

G.f.: (13 - 15*x)/(1 - x)^3.

E.g.f.: (13 + 11*x - x^2)*exp(x).

a(n) = -(n+1)*A023455(n).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

Mathematica

Table[13+12n-n^2, {n, 0, 70}] (* or *) LinearRecurrence[{3, -3, 1}, {13, 24, 33}, 70] (* Harvey P. Dale, Aug 31 2018 *)

Prog

(PARI) a(n)=13+12*n-n^2 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A023455.

Sequence in context: A119410 A098927 A133785 * A063315 A104342 A119590

Adjacent sequences: A136313 A136314 A136315 * A136317 A136318 A136319

Keyword

sign,easy

Author

N. J. A. Sloane, Apr 20 2008

Status

approved