login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A226517 Number of (19,14)-reverse multiples with n digits. 4
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 2, 1, 2, 1, 3, 2, 4, 3, 6, 4, 8, 5, 11, 7, 15, 10, 21, 14, 29, 19, 40, 26, 55, 36, 76, 50, 105, 69, 145, 95, 200, 131, 276, 181, 381, 250, 526, 345, 726, 476, 1002, 657, 1383, 907, 1909, 1252, 2635, 1728, 3637, 2385, 5020, 3292, 6929, 4544, 9564, 6272, 13201, 8657, 18221 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,15

COMMENTS

Comment from Emeric Deutsch, Aug 21 2016 (Start):

Given an increasing sequence of positive integers S = {a0, a1, a2, ... }, let

          F(x) = x^{a0} + x^{a1} + x^{a2} + ... .

Then the g. f. for the number of palindromic compositions of n with parts in S is (see Hoggatt and Bicknell, Fibonacci Quarterly, 13(4), 1975, 350 - 356):

      (1 + F(x))/(1 - F(x^2))

Playing with this, I have found easily that

1. number of palindromic compositions of n into {3,4,5,...} = A226916(n+4);

2. number of palindromic compositions of n into {1,4,7,10,13,...} = A226916(n+6);

3. number of palindromic compositions of n into {1,4} = A226517(n+10);

4. number of palindromic compositions of n into {1,5} = A226516(n+11).

(End)

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, 2178 And All That, Fib. Quart., 52 (2014), 99-120.

Index entries for linear recurrences with constant coefficients, signature (0,1,0,0,0,0,0,1).

FORMULA

G.f.: x^6*(1-x^2+x^4+x^5)/(1-x^2-x^8).

a(n) = a(n-2) + a(n-8) for n>11, with initial values a(0)-a(11) =  0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1. [Bruno Berselli, Jun 17 2013]

MAPLE

f:=proc(n) option remember;

if

n <= 5 then 0

elif n=6 then 1

elif n <= 9 then 0

elif n <= 11 then 1

else f(n-2)+f(n-8)

fi;

end;

[seq(f(n), n=0..120)];

MATHEMATICA

CoefficientList[Series[x^6 (1 - x^2 + x^4 + x^5) / (1 - x^2 - x^8), {x, 0, 80}], x] (* Vincenzo Librandi, Jun 18 2013 *)

LinearRecurrence[{0, 1, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1}, 80] (* Harvey P. Dale, Aug 23 2019 *)

CROSSREFS

Cf. A214927, A226516, A226916.

Sequence in context: A161053 A161257 A161282 * A185214 A241719 A269572

Adjacent sequences:  A226514 A226515 A226516 * A226518 A226519 A226520

KEYWORD

nonn,easy,base

AUTHOR

N. J. A. Sloane, Jun 16 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 24 09:40 EST 2020. Contains 332209 sequences. (Running on oeis4.)