login
A332187
a(n) = 8*(10^(2n+1)-1)/9 - 10^n.
3
7, 878, 88788, 8887888, 888878888, 88888788888, 8888887888888, 888888878888888, 88888888788888888, 8888888887888888888, 888888888878888888888, 88888888888788888888888, 8888888888887888888888888, 888888888888878888888888888, 88888888888888788888888888888, 8888888888888887888888888888888
OFFSET
0,1
FORMULA
a(n) = 8*A138148(n) + 7*10^n = A002282(2n+1) - 10^n.
G.f.: (7 + 101*x - 900*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
A332187 := n -> 8*(10^(2*n+1)-1)/9-10^n;
MATHEMATICA
Array[8 (10^(2 # + 1)-1)/9 - 10^# &, 15, 0]
LinearRecurrence[{111, -1110, 1000}, {7, 878, 88788}, 20] (* Harvey P. Dale, Jul 21 2024 *)
PROG
(PARI) apply( {A332187(n)=10^(n*2+1)\9*8-10^n}, [0..15])
(Python) def A332187(n): return 10**(n*2+1)//9*8-10**n
CROSSREFS
Cf. (A077776-1)/2 = A183190: indices of primes.
Cf. A002275 (repunits R_n = (10^n-1)/9), A002282 (8*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits only), A002113 (palindromes).
Cf. A332117 .. A332197 (variants with different "wing" digit 1, ..., 9).
Cf. A332180 .. A332189 (variants with different middle digit 0, ..., 9).
Sequence in context: A308296 A193342 A298301 * A093171 A330295 A177908
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 08 2020
STATUS
approved