OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
T. Etzion, On the stopping redundancy of Reed-Muller codes, IEEE Trans. Information Theory 52 (11) (2006) 4867-4879, also, arXiv:cs/0511056 [cs.IT], 2005.
Toufik Mansour and Armend Sh. Shabani, Bargraphs in bargraphs, Turkish Journal of Mathematics (2018) Vol. 42, Issue 5, 2763-2773.
Index entries for linear recurrences with constant coefficients, signature (4,-3,-4,4).
FORMULA
G.f.: 1/((1-x^2)*(1-2*x)^2).
a(n+1) - 2*a(n) = A000975(n+2) (n-th number without consecutive equal binary digits)
a(n) + a(n+1) = A000337(n+2);
a(n+1) - a(n) = A045883(n+2);
a(n+2) - a(n) = A001787(n+3) ( Number of edges in n-dimensional hypercube );
a(n+2) - 2*a(n+1) + a(n) = A059570(n+3);
Convolution of "Number of fixed points in all 231-avoiding involutions in S_n" (A059570) with the natural numbers (A000027), treating the result as if offset=0. - Graeme McRae, Jul 12 2006
Equals triangle A059260 * A008574 as a vector, where A008574 = [1, 4, 8, 12, 16, 20, ...]. - Gary W. Adamson, Mar 06 2012
MATHEMATICA
Table[((3n+1)*2^(n+3) + 9 + (-1)^n)/18, {n, 0, 50}] (* G. C. Greubel, Sep 27 2017 *)
LinearRecurrence[{4, -3, -4, 4}, {1, 4, 13, 36}, 50] (* Vincenzo Librandi, Nov 21 2018 *)
PROG
(PARI) a(n)=((3*n+1)*2^(n+3)+9+(-1)^n)/18 \\ Charles R Greathouse IV, Oct 16 2015
(Magma) [((3*n+1)*2^(n+3)+9+(-1)^n)/18: n in [0..40]]; // Vincenzo Librandi, Nov 21 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Creighton Dement, Feb 20 2005
STATUS
approved