A272525 Convolution of nonzero repunits (A002275) with themselves.

1, 22, 343, 4664, 58985, 713306, 8367627, 96021948, 1083676269, 12071330590, 133058984911, 1454046639232, 15775034293553, 170096021947874, 1824417009602195, 19478737997256516, 207133058984910837, 2194787379972565158, 23182441700960219479, 244170096021947873800

Offset: 0

Author

Ilya Gutkovskiy, May 02 2016

Keywords

• base
• nonn
• easy

Comments

Partial sums of A014925.

Links

• Eric Weisstein's World of Mathematics, Repunit
• Index entries for linear recurrences with constant coefficients, signature (22,-141,220,-100)

Crossrefs

Cf. A002275, A010879, A014925, A083449.

Programs

Mathematica

LinearRecurrence[{22, -141, 220, -100}, {1, 22, 343, 4664}, 20]
Table[(9 n (10^(n + 2) + 1) + 7 10^(n + 2) + 29)/729, {n, 0, 19}]

PARI

A272525(n)=(9*n+7)*(10^(n+2)+1)\729+1 \\ M. F. Hasler, Nov 02 2016

Formula

O.g.f.: 1/((1 - 10*x)^2*(1 - x)^2).

E.g.f.: (29 + 9*x + 700*exp(9*x) + 9000*x*exp(9*x))*exp(x)/729.

a(n) = 22*a(n-1) - 141*a(n-2) + 220*a(n-3) - 100*a(n-4).

a(n) = (9*n(10^(n+2) + 1) + 7*10^(n+2) + 29)/729.

A010879(a(n)) = A010879(n+1).