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 A332141 a(n) = 4*(10^(2*n+1)-1)/9 - 3*10^n. 2
 1, 414, 44144, 4441444, 444414444, 44444144444, 4444441444444, 444444414444444, 44444444144444444, 4444444441444444444, 444444444414444444444, 44444444444144444444444, 4444444444441444444444444, 444444444444414444444444444, 44444444444444144444444444444, 4444444444444441444444444444444 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..15. Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000). FORMULA a(n) = 4*A138148(n) + 1*10^n = A002278(2n+1) - 3*10^n. G.f.: (1 + 303*x - 700*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 A332141 := 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}, {1, 414, 44144}, 20] (* or *) Table[ FromDigits[Join[PadRight[{}, n, 4], {1}, PadRight[{}, n, 4]]], {n, 0, 20}](* Harvey P. Dale, Aug 17 2020 *) PROG (PARI) apply( {A332141(n)=10^(n*2+1)\9*4-3*10^n}, [0..15]) (Python) def A332141(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. A332121 .. A332191 (variants with different repeated digit 2, ..., 9). Cf. A332140 .. A332149 (variants with different middle digit 0, ..., 9). Sequence in context: A236149 A231312 A210304 * A187864 A190028 A184545 Adjacent sequences: A332138 A332139 A332140 * A332142 A332143 A332144 KEYWORD nonn,base,easy AUTHOR M. F. Hasler, Feb 09 2020 STATUS approved

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Last modified May 20 11:05 EDT 2024. Contains 372712 sequences. (Running on oeis4.)