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A000861
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Numbers ending with a vowel in American English.
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13
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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, 55, 59, 61, 62, 63, 65, 69, 71, 72, 73, 75, 79, 81, 82, 83, 85, 89, 91, 92, 93, 95, 99, 101, 102, 103, 105, 109, 112, 121, 122, 123, 125, 129, 131, 132, 133, 135, 139, 141, 142
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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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
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LINKS
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Index entries for linear recurrences with constant coefficients, 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).
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FORMULA
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a(n) = a(n-1) + a(n-46) - a(n-47) for n > 48.
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)
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PROG
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(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
(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
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CROSSREFS
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Cf. A247359 (complement), A152592 (characteristic fct of the complement), A059437 (a variant of the latter: vowels or "y").
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KEYWORD
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word,nonn,easy
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AUTHOR
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EXTENSIONS
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Corrected by Logan K. Young (lkyfella(AT)yahoo.com), Mar 19 2005
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 20 2006
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STATUS
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approved
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