A182190 a(n) = 6*a(n-1) - a(n-2) + 4 with n > 1, a(0)=0, a(1)=4.

0, 4, 28, 168, 984, 5740, 33460, 195024, 1136688, 6625108, 38613964, 225058680, 1311738120, 7645370044, 44560482148, 259717522848, 1513744654944, 8822750406820, 51422757785980, 299713796309064

Offset

0,2

Comments

Also, nonnegative m such that 2m(m+2)+1 is a square. - Bruno Berselli, Oct 22 2012

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

G.f.: 4*x/((1-x)*(1-6*x+x^2)). - Bruno Berselli, Jun 07 2012

a(n) = 4*A053142(n). - Bruno Berselli, Jun 07 2012

a(n) = A001653(n+1) - 1. - Kiran S. Kedlaya, Mar 14 2021

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

a(n) = A143608(n)*A143608(n+1). - R. J. Mathar, Jan 31 2024

a(n)-a(n-1) = A005319(n). - R. J. Mathar, Jan 31 2024

Mathematica

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

Prog

(Magma) I:=[0, 4]; [n le 2 select I[n] else 6*Self(n-1)-Self(n-2)+4: n in [1..20]]; // Bruno Berselli, Jun 07 2012
(Sage) [lucas_number1(2*n+1, 2, -1) -1 for n in (0..40)] # G. C. Greubel, May 24 2021

Crossrefs

Cf. A000129, A182189, A182431.

Sequence in context: A270943 A320527 A272281 * A317232 A272456 A125687

Adjacent sequences: A182187 A182188 A182189 * A182191 A182192 A182193

Keyword

nonn,easy

Author

Kenneth J Ramsey, Apr 17 2012

Status

approved