|
|
A092521
|
|
a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3).
|
|
20
|
|
|
1, 8, 56, 385, 2640, 18096, 124033, 850136, 5826920, 39938305, 273741216, 1876250208, 12860010241, 88143821480, 604146740120, 4140883359361, 28382036775408, 194533374068496, 1333351581704065, 9138927697859960
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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.
|
|
LINKS
|
|
|
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) = (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 *)
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
|
Cf. A212336 for more sequences with g.f. of the type 1/(1 - k*x + k*x^2 - x^3).
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
K. S. Bhanu (bhanu_105(AT)yahoo.com) and M. N. Deshpande, Apr 06 2004
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|