A280154 a(n) = 5*Lucas(n).

10, 5, 15, 20, 35, 55, 90, 145, 235, 380, 615, 995, 1610, 2605, 4215, 6820, 11035, 17855, 28890, 46745, 75635, 122380, 198015, 320395, 518410, 838805, 1357215, 2196020, 3553235, 5749255, 9302490, 15051745, 24354235, 39405980, 63760215, 103166195, 166926410, 270092605, 437019015

Offset

0,1

Comments

Fibonacci sequence beginning 10, 5.

After 5, the sequence provides the 3rd column of the rectangular array in A213590.

After 5, all terms belong to A191921 because a(n) = Lucas(n+4) - 3*Lucas(n-1).

From G. C. Greubel, Dec 27 2016: (Start)

{a(n) mod 3} yields (1,2,0,2,2,1,0,1), repeated, and is given as A082115.

{a(n) mod 6} yields (4,5,3,2,5,1,0,1,1,2,3,5,2,1,3,4,1,5,0,5,5,4,3,1) and is given as A082117. (End)

Links

Bruno Berselli, Table of n, a(n) for n = 0..1000

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (1,1).

Formula

G.f.: 5*(2 - x)/(1 - x - x^2).

a(n) = a(n-1) + a(n-2) for n>1.

a(n) = Fibonacci(n+5) + Fibonacci(n-5), with Fibonacci(-k) = -(-1)^k*Fibonacci(k) for the negative indices.

Maple

F := n -> combinat:-fibonacci(n):
seq(F(n+5) + F(n-5), n=0..38); # Peter Luschny, Dec 29 2016

Mathematica

Table[5 LucasL[n], {n, 0, 40}]

Prog

(PARI) vector(40, n, n--; fibonacci(n+5)+fibonacci(n-5))
(Magma) [5*Lucas(n): n in [0..40]];
(Sage)
def A280154():
    x, y = 10, 5
    while True:
        yield x
        x, y = y, x + y
a = A280154(); print([next(a) for _ in range(39)]) # Peter Luschny, Dec 29 2016

Crossrefs

Subsequence of A084176.

Cf. A022088: 5*Fibonacci(n).

Cf. A022359: Lucas(n+5) + Lucas(n-5).

Cf. A000032, A000045, A191921, A213590.

Cf. sequences with formula Fibonacci(n+k) + Fibonacci(n-k): A006355 (k=0, without the initial 1), A000032 (k=1), A022086 (k=2), A022112 (k=3, with an initial 4), A022090 (k=4), this sequence (k=5), A022352 (k=6).

Sequence in context: A083950 A045617 A158486 * A040093 A046797 A147675

Adjacent sequences: A280151 A280152 A280153 * A280155 A280156 A280157

Keyword

nonn,easy

Author

Bruno Berselli, Dec 27 2016

Status

approved