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A272525
Convolution of nonzero repunits (A002275) with themselves.
13
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
Eric Weisstein's World of Mathematics, Repunit
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
KEYWORD
base,nonn,easy
AUTHOR
Ilya Gutkovskiy, May 02 2016
STATUS
approved