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A092521 a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3). 17
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.

Partial sums of Chebyshev sequence S(n,7)=U(n,7/2) = A004187(n+1). - Wolfdieter Lang, Aug 31 2004

LINKS

Table of n, a(n) for n=1..20.

C. Pita, On s-Fibonomials, J. Int. Seq. 14 (2011) # 11.3.7

Index entries for sequences related to Chebyshev polynomials.

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) = -1/5+(3/5)*(7/2-(3/2)*sqrt(5))^n-(4/15)*(7/2-(3/2)*sqrt(5))^n*sqrt(5)+(4/15)*sqrt(5)*(7/2 +(3/2)*sqrt(5))^n+(3/5)*(7/2+(3/2)*sqrt(5))^n. - Paolo P. Lava, Jul 08 2008

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

Cf. A212336 for more sequences with g.f. of the type 1/(1 - k*x + k*x^2 - x^3).

Sequence in context: A057084 A101596 * A156088 A002914 A001666 A214942

Adjacent sequences:  A092518 A092519 A092520 * A092522 A092523 A092524

KEYWORD

nonn,easy

AUTHOR

K. S. Bhanu (bhanu_105(AT)yahoo.com) and M. N. Deshpande, Apr 06 2004

EXTENSIONS

Edited and extended by Robert G. Wilson v, Apr 08 2004

STATUS

approved

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Last modified November 19 14:52 EST 2018. Contains 317352 sequences. (Running on oeis4.)