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A226516 Number of (18,7)-reverse multiples with n digits. 4
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 3, 3, 4, 4, 6, 5, 8, 6, 10, 8, 13, 11, 17, 15, 23, 20, 31, 26, 41, 34, 54, 45, 71, 60, 94, 80, 125, 106, 166, 140, 220, 185, 291, 245, 385, 325, 510, 431, 676, 571, 896, 756, 1187, 1001, 1572, 1326, 2082, 1757, 2758, 2328, 3654, 3084, 4841, 4085, 6413 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,17

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 (0,1,0,0,0,0,0,0,0,1).

FORMULA

G.f.: x^6*(1-x^2+x^5+x^6)/(1-x^2-x^10).

a(n) = a(n-2) + a(n-10) for n>12, with initial values a(0)-a(12) equal to 0, 0, 0, 0, 0, 0, 1, 0, 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 <= 10 then 0

elif n <= 12 then 1

else f(n-2)+f(n-10)

fi;

end;

[seq(f(n), n=0..100)]

MATHEMATICA

CoefficientList[Series[x^6 (1 - x^2 + x^5 + x^6) / (1 - x^2 - x^10), {x, 0, 80}], x] (* Vincenzo Librandi, Jun 18 2013 *)

LinearRecurrence[{0, 1, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1}, 80] (* Harvey P. Dale, Jun 17 2015 *)

CROSSREFS

Cf. A214927, A226517, A226916.

Sequence in context: A161054 A161258 A161283 * A002300 A350063 A049099

Adjacent sequences:  A226513 A226514 A226515 * A226517 A226518 A226519

KEYWORD

nonn,easy,base

AUTHOR

N. J. A. Sloane, Jun 16 2013

STATUS

approved

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Last modified October 2 01:30 EDT 2022. Contains 357191 sequences. (Running on oeis4.)