A323824 a(0) = 6; thereafter a(n) = 4*a(n-1) + 1.

6, 25, 101, 405, 1621, 6485, 25941, 103765, 415061, 1660245, 6640981, 26563925, 106255701, 425022805, 1700091221, 6800364885, 27201459541, 108805838165, 435223352661, 1740893410645, 6963573642581, 27854294570325, 111417178281301, 445668713125205

Offset: 0

Author

N. J. A. Sloane, Feb 01 2019

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Mike Warburton, Ulam-Warburton Automaton - Counting Cells with Quadratics, arXiv:1901.10565 [math.CO], 2019.
• Index entries for linear recurrences with constant coefficients, signature (5,-4).

Crossrefs

Cf. A178415, A347834.

Programs

Mathematica

A323824[n_]:=(19*4^n-1)/3;Array[A323824,30,0] (* or *)
LinearRecurrence[{5,-4},{6,25},30] (* Paolo Xausa, Nov 14 2023 *)
NestList[4#+1&,6,30] (* Harvey P. Dale, Nov 26 2024 *)

PARI

Vec((6 - 5*x) / ((1 - x)*(1 - 4*x)) + O(x^25)) \\ Colin Barker, Feb 01 2019

PARI

a(n) = (19*4^n - 1) / 3 \\ Colin Barker, Feb 01 2019

Formula

G.f.: (6 - 5*x) / ((1 - x)*(1 - 4*x)).

a(n) = (19*4^n - 1) / 3. - Colin Barker, Feb 01 2019

a(n) = A178415(7, n) = A347834(10, n-1), arrays, for n >= 1. - Wolfdieter Lang, Nov 29 2021