OFFSET
0,3
COMMENTS
Binomial transform of A005408 (with interpolated zeros). Binomial transform is A087448. a(n+2) = 2*A045623(n+1); a(n+1) = A001792(n) + (0^n - (-2)^n)/2. The sequence 1,4,10,... given by 2^n*(n+3)/2 - 0^n/2 is the binomial transform of 1,3,3,5,5,...
Equals real part of binomial transform of [1, 2*i, 3, 4*i, 5, 6*i, ...]; i=sqrt(-1). - Gary W. Adamson, Sep 21 2008
An elephant sequence, see A175655. For the central square 24 A[5] vectors, with decimal values between 27 and 432, lead to this sequence (without the first leading 1). For the corner squares these vectors lead to the companion sequence A057711 (without the leading 0). - Johannes W. Meijer, Aug 15 2010
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..3000
Paul Barry, A Catalan Transform and Related Transformations on Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5.
Index entries for linear recurrences with constant coefficients, signature (4,-4).
FORMULA
a(n) = Sum_{k=0..floor(n/2)} binomial(n, 2k)*(2k+1). - Paul Barry, Nov 29 2004
From Colin Barker, Mar 23 2012: (Start)
G.f.: (1-x)*(1-2*x+2*x^2)/(1-2*x)^2.
a(n) = 4*a(n-1) - 4*a(n-2) for n > 3. (End)
E.g.f.: (1 - x + exp(2*x)*(1 + x))/2. - Stefano Spezia, Jan 31 2023
MATHEMATICA
Join[{1, 1}, Table[(n + 2) 2^(n - 2), {n, 2, 30}]] (* Harvey P. Dale, Feb 22 2011 *)
PROG
(Python)
def A087447(n): return n+2<<n-2 if n>1 else 1 # Chai Wah Wu, Oct 03 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Sep 05 2003
EXTENSIONS
Definition corrected (by a factor of 2) by R. J. Mathar, Feb 21 2009
STATUS
approved