cp's OEIS Frontend

A226916 Number of (17,11)-reverse multiples with n digits.

%I A226916 #19 Jan 09 2025 10:14:34
%S A226916 0,0,0,0,1,0,0,1,1,1,2,1,2,2,3,3,5,4,7,6,10,9,15,13,22,19,32,28,47,41,
%T A226916 69,60,101,88,148,129,217,189,318,277,466,406,683,595,1001,872,1467,
%U A226916 1278,2150,1873,3151,2745,4618,4023,6768,5896,9919,8641,14537,12664,21305,18560,31224,27201,45761
%N A226916 Number of (17,11)-reverse multiples with n digits.
%C A226916 Comment from _Emeric Deutsch_, Aug 21 2016 (Start):
%C A226916 Given an increasing sequence of positive integers S = {a0, a1, a2, ... }, let
%C A226916           F(x) = x^{a0} + x^{a1} + x^{a2} + ... .
%C A226916 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):
%C A226916       (1 + F(x))/(1 - F(x^2))
%C A226916 Playing with this, I have found easily that
%C A226916 1. number of palindromic compositions of n into {3,4,5,...} = A226916(n+4);
%C A226916 2. number of palindromic compositions of n into {1,4,7,10,13,...} = A226916(n+6);
%C A226916 3. number of palindromic compositions of n into {1,4} = A226517(n+10);
%C A226916 4. number of palindromic compositions of n into {1,5} = A226516(n+11).
%C A226916 (End)
%H A226916 Vincenzo Librandi, <a href="/A226916/b226916.txt">Table of n, a(n) for n = 0..1000</a>
%H A226916 V. E. Hogatt, M. Bicknell, <a href="https://fq.math.ca/13-4.html">Palindromic Compositions</a>, Fib. Quart. 13 (4) (1975) 350-356
%H A226916 N. J. A. Sloane, <a href="http://arxiv.org/abs/1307.0453">2178 And All That</a>, Fib. Quart., 52 (2014), 99-120.
%H A226916 N. J. A. Sloane, <a href="/A001232/a001232.pdf">2178 And All That</a> [Local copy]
%H A226916 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,0,0,1).
%F A226916 G.f.: x^4*(1+x)*(1-x+x^3)/(1-x^2-x^6).
%F A226916 a(2n) = A058278(n-1). a(2n+1)=A000930(n-3). - _R. J. Mathar_, Dec 13 2022
%t A226916 CoefficientList[Series[x^4 (1 - x^2 + x^3 + x^4) / (1 - x^2 - x^6), {x, 0, 70}], x] (* _Vincenzo Librandi_, Jul 16 2013 *)
%Y A226916 Cf. A214927, A226516, A226517.
%K A226916 nonn,base,easy
%O A226916 0,11
%A A226916 _N. J. A. Sloane_, Jun 24 2013