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
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
Programs
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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
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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
Comments