login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A203170 Sum of the fourth powers of the first n odd-indexed Fibonacci numbers. 3
0, 1, 17, 642, 29203, 1365539, 64107780, 3011403301, 141469813301, 6646055880582, 312223061019703, 14667837157106759, 689076118833981960, 32371909717271872585, 1520790680382055836761, 71444790066793903279242 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Natural bilateral extension (brackets mark index 0): ..., -1365539, -29203, -642, -17, -1, [0], 1, 17, 642, 29203, 1365539, ...  That is, a(-n) = -a(n).

LINKS

Table of n, a(n) for n=0..15.

FORMULA

Let F(n) be the Fibonacci number A000045(n).

a(n) = Sum_{k=1..n} F(2k-1)^4.

Closed form: a(n) = (1/75)(F(8n) + 12 F(4n) + 18 n).

Recurrence: a(n) - 56 a(n-1) + 440 a(n-2) - 770 a(n-3) + 440 a(n-4) - 56 a(n-5) + a(n-6) = 0.

G.f.: A(x) = (x - 39 x^2 + 130 x^3 - 39 x^4 + x^5)/(1 - 56 x + 440 x^2 - 770 x^3 + 440 x^4 - 56 x^5 + x^6) = x(1 - 39 x + 130 x^2 - 39 x^3 + x^4)/((1 - x)^2 (1 - 7 x + x^2)(1 - 47 x + x^2)).

MATHEMATICA

a[n_Integer] := (1/75)(Fibonacci[8n] + 12*Fibonacci[4n] + 18 n); Table[a[n], {n, 0, 20}]

CROSSREFS

Cf. A203169, A203171, A203172.

Cf. A001906, A103433, A163200.

Sequence in context: A219075 A265678 A200907 * A063941 A089018 A118769

Adjacent sequences:  A203167 A203168 A203169 * A203171 A203172 A203173

KEYWORD

nonn,easy

AUTHOR

Stuart Clary, Dec 30 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 15 01:25 EST 2019. Contains 329143 sequences. (Running on oeis4.)