The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A297832 Solution of the complementary equation a(n) = a(1)*b(n-1) - a(0)*b(n-2) + 2*n - 2, where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, and (b(n)) is the increasing sequence of positive integers not in (a(n)). See Comments. 5

%I #8 Nov 06 2018 12:46:28

%S 1,2,7,10,13,18,20,25,27,32,34,37,40,45,49,51,54,57,62,66,68,71,74,79,

%T 83,85,90,92,97,99,102,105,110,112,115,120,124,126,131,133,138,140,

%U 143,146,151,153,156,161,165,167,172,174,179,181,184,187,192,194

%N Solution of the complementary equation a(n) = a(1)*b(n-1) - a(0)*b(n-2) + 2*n - 2, where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, and (b(n)) is the increasing sequence of positive integers not in (a(n)). See Comments.

%C The increasing complementary sequences a() and b() are uniquely determined by the titular equation and initial values. See A297830 for a guide to related sequences.

%C a(n) - (2+sqrt(2))*n < 2 for n >= 1.

%H Clark Kimberling, <a href="/A297832/b297832.txt">Table of n, a(n) for n = 0..10000</a>

%e a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, so that a(2) = 7.

%e Complement: (b(n)) = (3,4,5,7,8,10,12,13,15,17,18,19,...)

%t a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4;

%t a[n_] := a[n] = a[1]*b[n - 1] - a[0]*b[n - 2] + 2 n - 2;

%t j = 1; While[j < 100, k = a[j] - j - 1;

%t While[k < a[j + 1] - j + 1, b[k] = j + k + 2; k++]; j++]; k

%t Table[a[n], {n, 0, k}] (* A297832 *)

%Y Cf. A297826, A297830.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Feb 04 2018

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 29 13:48 EDT 2024. Contains 372942 sequences. (Running on oeis4.)