OFFSET
0,4
COMMENTS
Apparently the same as A001045 after the first term. - R. J. Mathar, Nov 27 2008 [This conjecture is true. - Peter Luschny, Nov 28 2019]
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Forrest M. Hilton, Finite Dynamical Laminations, arXiv:2408.01353 [math.DS], 2024. See p. 16.
Index entries for linear recurrences with constant coefficients, signature (1,2).
FORMULA
From Sergei N. Gladkovskii, May 22 2013 and Sep 09 2013: (Start)
G.f.: 1 + A(x) where A(x) is the g.f. of A001045.
G.f.: 1 + Q(0)/3, where Q(k)= 1 - 1/(4^k - 2*x*16^k/(2*x*4^k - 1/(1 + 1/(2*4^k - 8*x*16^k/(4*x*4^k + 1/Q(k+1)))))); (continued fraction).
G.f.: 1+ Q(0)*x/2 , where Q(k) = 1 + 1/(1 - x*(2*k+1 + 2*x)/( x*(2*k+2 + 2*x) + 1/Q(k+1) )); (continued fraction). (End)
From Colin Barker, Nov 28 2019: (Start)
a(n) = a(n-1) + 2*a(n-2) for n>2.
a(n) = ((-1)^(1 + n) + 2^n)/ 3 for n>0. (End)
E.g.f.: (3 - exp(-x) + exp(2*x))/3. - Stefano Spezia, Feb 13 2020
MATHEMATICA
a[n_] := Product[(1 + 8 Cos[k Pi/n]^2), {k, 1, Floor[(n - 1)/2]}];
Table[Round[a[n]], {n, 0, 20}]
PROG
(PARI) Vec((1 - 2*x^2) / ((1 + x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, Nov 28 2019
(PARI) apply( {A152046(n)=2^n\/3+!n}, [0..40]) \\ M. F. Hasler, Feb 13 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Nov 21 2008
EXTENSIONS
Edited by Peter Luschny, Nov 28 2019
STATUS
approved