cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A332149 a(n) = 4*(10^(2*n+1)-1)/9 + 5*10^n.

Original entry on oeis.org

9, 494, 44944, 4449444, 444494444, 44444944444, 4444449444444, 444444494444444, 44444444944444444, 4444444449444444444, 444444444494444444444, 44444444444944444444444, 4444444444449444444444444, 444444444444494444444444444, 44444444444444944444444444444, 4444444444444449444444444444444
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002278 (4*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332119 .. A332189 (variants with different repeated digit 1, ..., 8).
Cf. A332140 .. A332148 (variants with different middle digit 0, ..., 8).

Programs

  • Maple
    A332149 := n -> 4*(10^(2*n+1)-1)/9+5*10^n;
  • Mathematica
    Array[4 (10^(2 # + 1)-1)/9 + 5*10^# &, 15, 0]
  • PARI
    apply( {A332149(n)=10^(n*2+1)\9*4+5*10^n}, [0..15])
  • Python
    def A332149(n): return 10**(n*2+1)//9*4+5*10**n

Formula

a(n) = 4*A138148(n) + 9*10^n = A002278(2n+1) + 5*10^n.
G.f.: (9 - 505*x + 100*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.
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