A332170 a(n) = 7*(10^(2n+1)-1)/9 - 7*10^n.

0, 707, 77077, 7770777, 777707777, 77777077777, 7777770777777, 777777707777777, 77777777077777777, 7777777770777777777, 777777777707777777777, 77777777777077777777777, 7777777777770777777777777, 777777777777707777777777777, 77777777777777077777777777777, 7777777777777770777777777777777

Offset: 0

Author

M. F. Hasler, Feb 08 2020

Keywords

• nonn
• base
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002281 (7*R_n), A011557 (10^n).

Cf. A138148 (cyclops numbers with binary digits only), A002113 (palindromes).

Cf. A332120 .. A332190 (variants with different repeated digit 2, ..., 9).

Cf. A332171 .. A332179 (variants with different middle digit 1, ..., 9).

Programs

Maple

A332170 := n -> 7*(10^(2*n+1)-1)/9-7*10^n;

Mathematica

Array[7 ((10^(2 # + 1)-1)/9 - 10^#) &, 15, 0]

PARI

apply( {A332170(n)=(10^(n*2+1)\9-10^n)*7}, [0..15])

Python

def A332170(n): return (10**(n*2+1)//9-10^n)*7

Formula

a(n) = 7*A138148(n) = A002281(2n+1) - 7*A011557(n).

G.f.: 7*x*(101 - 200*x)/((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.