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A332149
a(n) = 4*(10^(2*n+1)-1)/9 + 5*10^n.
9
9, 494, 44944, 4449444, 444494444, 44444944444, 4444449444444, 444444494444444, 44444444944444444, 4444444449444444444, 444444444494444444444, 44444444444944444444444, 4444444444449444444444444, 444444444444494444444444444, 44444444444444944444444444444, 4444444444444449444444444444444
OFFSET
0,1
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.
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]
PROG
(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
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).
Sequence in context: A157595 A042415 A277360 * A112910 A180585 A102909
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 09 2020
STATUS
approved