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

Author

Paul Curtz, May 21 2008

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (17,-16)

Crossrefs

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

Programs

Magma

[(1+2*16^n)/3: n in [0..20]]; // Vincenzo Librandi, Aug 09 2011

Mathematica

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

PARI

vector(20, n, n--; (1 + 2^(4*n+1))/3) \\ G. C. Greubel, Nov 03 2018

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)