A182188 A sequence of row differences for table A182119.

1, -1, -11, -69, -407, -2377, -13859, -80781, -470831, -2744209, -15994427, -93222357, -543339719, -3166815961, -18457556051, -107578520349, -627013566047, -3654502875937, -21300003689579

Offset

0,3

Comments

This is a list of row differences corresponding to a difference of 1 in table A182119, column 0. If A181119(k+1,0) - A182119(k,0) = 1, then a(n) = A182119(k+1,n) - A182119(k,n).

If p is a prime of the form 8*n +- 3, then a(p) == 3 (mod p). If p is a prime of the form 8*n +- 1, then a(p) == -1 (mod p).

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7,-7,1).

Formula

a(n) = 6*a(n-1) - a(n-2) - 4. [corrected by Klaus Purath, Mar 19 2021]

a(n) = -(A182189(n-1) + 2*A182190(n-1)).

a(n) = 2 - A182189(n).

From Klaus Purath, Mar 19 2021: (Start)

a(n) = 7*a(n-1) - 7*a(n-2) + a(n-3).

a(n) = (-1)*Sum_{i=1..2*n-1} A001333(i) for n > 0.

a(n) = 1 - A001542(n) for n > 0.

a(n) = 1 - 2*A001109(n) for n > 0.

a(n) = (-1)*A005409(2*n) for n > 0. (End)

G.f.: (1 - 8*x + 3*x^2)/((1-x)*(1-6*x+x^2)). - Chai Wah Wu, Apr 08 2021

a(n) = 1 - Pell(2*n), where Pell(n) = A000129(n). - G. C. Greubel, May 24 2021

Mathematica

m = 13; n = 3; c = 0;
list3 = Reap[While[c < 22, t = 6 n - m - 4; Sow[t]; m = n; n = t; c++]][[2, 1]]
Table[1 -Fibonacci[2*n, 2], {n, 0, 40}] (* G. C. Greubel, May 24 2021 *)

Prog

(Sage) [1 - lucas_number1(2*n, 2, -1) for n in (0..40)] # G. C. Greubel, May 24 2021

Crossrefs

Cf. A000129, A001109, A001333, A001542, A005409, A182189, A182190, A182119.

Sequence in context: A169731 A212057 A293550 * A099336 A236320 A211050

Adjacent sequences: A182185 A182186 A182187 * A182189 A182190 A182191

Keyword

sign,easy

Author

Kenneth J Ramsey, Apr 17 2012

Status

approved