A126719 a(n) = -n^2 + 9*n + 23.

23, 31, 37, 41, 43, 43, 41, 37, 31, 23, 13, 1, -13, -29, -47, -67, -89, -113, -139, -167, -197, -229, -263, -299, -337, -377, -419, -463, -509, -557, -607, -659, -713, -769, -827, -887, -949, -1013, -1079, -1147, -1217, -1289, -1363, -1439, -1517, -1597, -1679, -1763, -1849, -1937, -2027, -2119, -2213

Offset: 0

Author

Michael M. Ross, Mar 13 2007

Keywords

• sign
• easy

Comments

Derivation is similar to that of A126665, which see for further information.

Examples

			For n=8, -1*8^2 + 9*8 + 23 = 31.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Michael M. Ross, Natural Numbers.
• Robert Sacks, Number Spiral: Method of Common Differences.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A126665.

Programs

Maple

A126719:=n->-n^2+9*n+23: seq(A126719(n), n=0..100); # Wesley Ivan Hurt, Jan 20 2017

Mathematica

Table[-n^2+9n+23,{n,0,60}] (* or *) LinearRecurrence[{3,-3,1},{23,31,37},60] (* Harvey P. Dale, Oct 19 2011 *)

PARI

a(n)=-n^2+9*n+23 \\ Charles R Greathouse IV, Oct 07 2015

Formula

From Harvey P. Dale, Oct 19 2011: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), a(0)=23, a(1)=31, a(2)=37.

G.f.: ((38 - 13*x)*x - 23)/(x-1)^3. (End)

E.g.f.: exp(x)*(23 + 8*x - x^2). - Elmo R. Oliveira, Nov 02 2024