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A332145
a(n) = 4*(10^(2*n+1)-1)/9 + 10^n.
1
5, 454, 44544, 4445444, 444454444, 44444544444, 4444445444444, 444444454444444, 44444444544444444, 4444444445444444444, 444444444454444444444, 44444444444544444444444, 4444444444445444444444444, 444444444444454444444444444, 44444444444444544444444444444, 4444444444444445444444444444444
OFFSET
0,1
FORMULA
a(n) = 4*A138148(n) + 5*10^n = A002278(2n+1) + 10^n.
G.f.: (5 - 101*x - 300*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
A332145 := n -> 4*(10^(2*n+1)-1)/9+10^n;
MATHEMATICA
Array[4 (10^(2 # + 1)-1)/9 + 10^# &, 15, 0]
PROG
(PARI) apply( {A332145(n)=10^(n*2+1)\9*4+10^n}, [0..15])
(Python) def A332145(n): return 10**(n*2+1)//9*4+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. A332115 .. A332195 (variants with different repeated digit 1, ..., 9).
Cf. A332140 .. A332149 (variants with different middle digit 0, ..., 9).
Sequence in context: A300971 A300928 A221626 * A144509 A375262 A240700
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 09 2020
STATUS
approved