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%I #36 Apr 19 2024 01:58:47
%S 0,1,2,3,5,9,12,21,22,23,25,29,31,32,33,35,39,41,42,43,45,49,51,52,53,
%T 55,59,61,62,63,65,69,71,72,73,75,79,81,82,83,85,89,91,92,93,95,99,
%U 101,102,103,105,109,112,121,122,123,125,129,131,132,133,135,139,141,142
%N Numbers ending with a vowel in American English.
%C The German name of n ends in a vowel iff n==2 or n==3 (mod 100), so the German analog of this sequence would be {2, 3, 102, 103, 202, 203, ...}. - _M. F. Hasler_, Sep 20 2014
%H Vincenzo Librandi, <a href="/A000861/b000861.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_47">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).
%F From _Chai Wah Wu_, Apr 18 2024: (Start)
%F a(n) = a(n-1) + a(n-46) - a(n-47) for n > 48.
%F G.f.: x^2*(x^46 + 4*x^45 + 2*x^44 + x^43 + x^42 + 2*x^41 + 4*x^40 + 2*x^39 + x^38 + x^37 + 2*x^36 + 4*x^35 + 2*x^34 + x^33 + x^32 + 2*x^31 + 4*x^30 + 2*x^29 + x^28 + x^27 + 2*x^26 + 4*x^25 + 2*x^24 + x^23 + x^22 + 2*x^21 + 4*x^20 + 2*x^19 + x^18 + x^17 + 2*x^16 + 4*x^15 + 2*x^14 + x^13 + x^12 + 2*x^11 + 4*x^10 + 2*x^9 + x^8 + x^7 + 9*x^6 + 3*x^5 + 4*x^4 + 2*x^3 + x^2 + x + 1)/(x^47 - x^46 - x + 1). (End)
%o (PARI) print1(0",");for(n=1,3,for(k=10^(n-1),10^n-1,m100=k%100;m10=k%10;if(m100==12 || ((m100>20 || m100<10) && ((m10==1)||(m10==2)||(m10==3)||(m10==5)||(m10==9))),print1(k",")))) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 20 2006
%o (PARI) is(n,S=[1,2,3,5,9,12])=setsearch(S,if(n%100>19,n%10,n%100))||!n \\ Add 0 in S (and optionally remove trailing ||...) for the A059437 variant. Add "Set()" around [...] for PARI versions < 2.6. - _M. F. Hasler_, Sep 14 2014
%Y Cf. A247359 (complement), A152592 (characteristic fct of the complement), A059437 (a variant of the latter: vowels or "y").
%Y Cf. A247361 (French analog) and A247360 (complement).
%K word,nonn,easy,changed
%O 1,3
%A _N. J. A. Sloane_
%E Corrected by Logan K. Young (lkyfella(AT)yahoo.com), Mar 19 2005
%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 20 2006
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