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

0,2

Comments

Partial sums of A014925.

Links

Table of n, a(n) for n=0..19.

Eric Weisstein's World of Mathematics, Repunit

Index entries for linear recurrences with constant coefficients, signature (22,-141,220,-100)

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).

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}]

Prog

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

Crossrefs

Cf. A002275, A010879, A014925, A083449.

Sequence in context: A021254 A231647 A083449 * A277849 A277838 A277635

Adjacent sequences: A272522 A272523 A272524 * A272526 A272527 A272528

Keyword

base,nonn,easy

Author

Ilya Gutkovskiy, May 02 2016

Status

approved