A139792 First quadrisection of A139763 (1, 2, 3, 4, 11, ...).

1, 11, 171, 2731, 43691, 699051, 11184811, 178956971, 2863311531, 45812984491, 733007751851, 11728124029611, 187649984473771, 3002399751580331, 48038396025285291, 768614336404564651, 12297829382473034411, 196765270119568550571, 3148244321913096809131

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (17,-16)

Formula

a(n) = 16*a(n-1) - 5.

a(n) = 10*A131865(n) + 1.

G.f.: ( 1-6*x ) / ( (16*x-1)*(x-1) ). - R. J. Mathar, Feb 06 2011

E.g.f.: (exp(x) + 2*exp(16*x))/3. - G. C. Greubel, Nov 03 2018

From Jianing Song, Aug 30 2022: (Start)

a(n) = A001045(4*n+1).

a(n+1) - a(n) = 10*A001025(n). (End)

Mathematica

Table[(1 + 2^(4*n+1))/3, {n, 0, 20}] (* G. C. Greubel, Nov 03 2018 *)

Prog

(Magma) [(1+2*16^n)/3: n in [0..20]]; // Vincenzo Librandi, Aug 09 2011
(PARI) vector(20, n, n--; (1 + 2^(4*n+1))/3) \\ G. C. Greubel, Nov 03 2018

Crossrefs

Second quadrisection of Jacobsthal numbers A001045; the other quadrisections are A195156 (first), A144864 (third), and A141060 (fourth).

Sequence in context: A381219 A205087 A064182 * A025758 A243677 A374302

Adjacent sequences: A139789 A139790 A139791 * A139793 A139794 A139795

Keyword

nonn,easy

Author

Paul Curtz, May 21 2008

Status

approved