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A332147
a(n) = 4*(10^(2*n+1)-1)/9 + 3*10^n.
1
7, 474, 44744, 4447444, 444474444, 44444744444, 4444447444444, 444444474444444, 44444444744444444, 4444444447444444444, 444444444474444444444, 44444444444744444444444, 4444444444447444444444444, 444444444444474444444444444, 44444444444444744444444444444, 4444444444444447444444444444444
OFFSET
0,1
FORMULA
a(n) = 4*A138148(n) + 7*10^n = A002278(2n+1) + 3*10^n.
G.f.: (7 - 303*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
A332147 := n -> 4*(10^(2*n+1)-1)/9+3*10^n;
MATHEMATICA
Array[4 (10^(2 # + 1)-1)/9 + 3*10^# &, 15, 0]
LinearRecurrence[{111, -1110, 1000}, {7, 474, 44744}, 20] (* Harvey P. Dale, Mar 08 2022 *)
PROG
(PARI) apply( {A332147(n)=10^(n*2+1)\9*4+3*10^n}, [0..15])
(Python) def A332147(n): return 10**(n*2+1)//9*4+3*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. A332117 .. A332197 (variants with different repeated digit 1, ..., 9).
Cf. A332140 .. A332149 (variants with different middle digit 0, ..., 9).
Sequence in context: A254966 A345455 A261806 * A278143 A119621 A142734
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 09 2020
STATUS
approved