A237415 For k in {2,3,...,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^3. This is k(2).

0, 1, 2, 8, 9, 10, 11, 12, 18, 19, 20, 21, 22, 28, 29, 30, 31, 32, 38, 39, 40, 41, 42, 48, 49, 50, 51, 52, 58, 59, 60, 61, 62, 68, 69, 70, 71, 72, 78, 79, 80, 81, 82, 88, 89, 90, 91, 92, 98, 99, 100, 101, 102, 108, 109, 110, 111, 112, 118, 119, 120, 121, 122, 128

Offset

0,3

Comments

Nonnegative integers m such that floor(2*m^2/10) = 2*floor(m^2/10). [Bruno Berselli, Dec 08 2015]

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Formula

G.f.: x*(1 + x + 6*x^2 + x^3 + x^4)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4)). [Bruno Berselli, Feb 08 2014]

a(n) = a(n-1)+a(n-5)-a(n-6). - Vincenzo Librandi, Feb 12 2014

Mathematica

LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 1, 2, 8, 9, 10}, 70] (* Bruno Berselli, Feb 08 2014 *)
CoefficientList[Series[x (1 + x + 6 x^2 + x^3 + x^4)/((1 - x)^2 (1 + x + x^2 + x^3 + x^4)), {x, 0, 100}], x] (* Vincenzo Librandi, Feb 12 2014 *)
NestList[If[Mod[#, 10]==2, FromDigits[Join[Most[IntegerDigits[#]], {8}]], #+ 1]&, 0, 100] (* Harvey P. Dale, Feb 21 2016 *)

Prog

(Magma) I:=[0, 1, 2, 8, 9, 10]; [n le 6 select I[n] else Self(n-1)+Self(n-5)-Self(n-6): n in [1..80]]; // Vincenzo Librandi, Feb 12 2014

Crossrefs

Cf. A235498, A235499, A237341 - A237346.

Sequence in context: A350762 A081101 A043059 * A247635 A152754 A001560

Adjacent sequences: A237412 A237413 A237414 * A237416 A237417 A237418

Keyword

nonn,base,easy

Author

Vincenzo Librandi, Feb 07 2014

Extensions

Definition by N. J. A. Sloane, Feb 07 2014

Status

approved