OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Jeremiah Bartz, Bruce Dearden, and Joel Iiams, Classes of Gap Balancing Numbers, arXiv:1810.07895 [math.NT], 2018.
Jeremiah Bartz, Bruce Dearden, and Joel Iiams, Counting families of generalized balancing numbers, The Australasian Journal of Combinatorics (2020) Vol. 77, Part 3, 318-325.
Index entries for linear recurrences with constant coefficients, signature (0,0,6,0,0,-1).
FORMULA
a(3n+1) = 7*A002315(n).
G.f.: (x+1)*(x^2+3*x+1)^2 / (x^6-6*x^3+1). - Colin Barker, Sep 14 2014
EXAMPLE
17 is in the sequence since sqrt((17^2 + 7^2)/2) = 13 is an integer.
MATHEMATICA
Column[LinearRecurrence[{0, 0, 6, 0, 0, -1}, {1, 7, 17, 23, 49, 103}, 35] ] (* Vincenzo Librandi, Jul 30 2017 *)
PROG
(PARI) Vec((x+1)*(x^2+3*x+1)^2/(x^6-6*x^3+1) + O(x^100)) \\ Colin Barker, Sep 14 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Henry Bottomley, Oct 05 2002
EXTENSIONS
More terms from Colin Barker, Sep 14 2014
STATUS
approved