OFFSET
1,2
COMMENTS
a(n) such that 9*(T(a(n)-1) + T(a(n+1)-1)) = 7*(T(a(n)+a(n+1)-1)), where T(i) denotes the i-th triangular number.
Partial sums of Chebyshev sequence S(n,7) = U(n,7/2) =A004187(n+1). -Wolfdieter Lang,Aug 31 2004
LINKS
Michael De Vlieger,Table of n, a(n) for n = 1..1197
Francesca Arici and Jens Kaad,Gysin sequences and SU(2)-symmetries of C*-algebras,arXiv:2012.11186 [math.OA], 2020.
C. Pita,On s-Fibonomials,J. Int. Seq. 14 (2011) # 11.3.7.
Index entries for linear recurrences with constant coefficients,signature (8,-8,1).
FORMULA
G.f.: x/(1 - 8*x + 8*x^2 - x^3) = x/((1 - x)*(1 - 7*x + x^2)).
a(n) = 7*a(n-1) - a(n-2) + 1, n>=2, a(0):=0, a(1)=1.
a(n) = (S(n, 7)-S(n-1, 7) -1)/5, n>=1, with S(n, 7)=U(n, 7/2)=A004187(n+1).
a(n) =A058038(n)/3.
a(n) = (1/3)*Sum_{k=0..n} Fibonacci(4*k). -Gary Detlefs,Dec 07 2010
MATHEMATICA
a[1] = 1; a[2] = 8; a[3] = 56; a[n_]:= a[n] = 8 a[n - 1] - 8 a[n - 2] + a[n - 3]; Table[ a[n], {n, 20}] (*Robert G. Wilson v,Apr 08 2004 *)
Table[(LucasL[4n+2]-3)/15, {n, 1, 20}] (*Vladimir Reshetnikov,Oct 28 2015 *)
LinearRecurrence[{8, -8, 1}, {1, 8, 56}, 30] (*Harvey P. Dale,Dec 27 2015 *)
PROG
(PARI) Vec(x/((1-x)*(1-7*x+x^2)) + O(x^100)) \\Altug Alkan,Oct 29 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
K. S. Bhanu (bhanu_105(AT)yahoo.com) and M. N. Deshpande, Apr 06 2004
EXTENSIONS
Edited and extended byRobert G. Wilson v,Apr 08 2004
STATUS
approved