A000861 Numbers ending with a vowel in American English.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• word
• nonn
• easy

Comments

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• 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).

Crossrefs

Cf. A247359 (complement), A152592 (characteristic fct of the complement), A059437 (a variant of the latter: vowels or "y").

Cf. A247361 (French analog) and A247360 (complement).

Programs

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

Formula

From Chai Wah Wu, Apr 18 2024: (Start)

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)

Extensions

Corrected by Logan K. Young (lkyfella(AT)yahoo.com), Mar 19 2005

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 20 2006