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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A113032 a(n) = Sum_{k=0..floor(n/8)} binomial(n-5*k, 3*k). 1
1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11, 21, 36, 57, 85, 121, 167, 228, 315, 449, 666, 1023, 1605, 2533, 3974, 6156, 9394, 14137, 21051, 31159, 46066, 68305, 101850, 152857, 230720, 349576, 530476, 804579, 1217951, 1838897, 2769267, 4161918, 6247570, 9375799 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

R. Austin and R. K. Guy, Binary sequences without isolated ones, Fib. Quart., 16 (1978), 84-86.

FORMULA

G.f.: (1-x)^2/(1-3*x-3*x^2-x^3-x^8).

EXAMPLE

a(10+1)=11 because C(10,0) + C(5,3) = 1+10 = 11.

MATHEMATICA

Table[Sum[Binomial[n - 5*k, 3*k], {k, 0, Floor[n/8]}], {n, 0, 50}] (* G. C. Greubel, Apr 09 2018 *)

PROG

(PARI) a(n) = sum(k=0, n\8, binomial(n-5*k, 3*k)); \\ Michel Marcus, Sep 05 2013

(PARI) lista(nn) = {my(x = xx + O(xx^nn)); gf = (1-x)^2/(1-3*x-3*x^2-x^3-x^8); for (i=0, nn-1, print1(polcoeff(gf, i, xx), ", ")); } \\ Michel Marcus, Sep 05 2013

(MAGMA) [(&+[Binomial(n-5*k, 3*k): k in [0..Floor(n/8)]]): n in [0..50]]; // G. C. Greubel, Apr 09 2018

CROSSREFS

Cf. A005251, A005253, A000045.

Sequence in context: A005575 A294745 A050407 * A100134 A137356 A103198

Adjacent sequences:  A113029 A113030 A113031 * A113033 A113034 A113035

KEYWORD

nonn

AUTHOR

Alexey Kistanov (plast(AT)solid.ru), Jan 05 2006

EXTENSIONS

Corrected by T. D. Noe, Nov 01 2006

More terms from Michel Marcus, Sep 05 2013

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified April 24 16:33 EDT 2018. Contains 303030 sequences. (Running on oeis4.)