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Sum_{i=1..(10^n - 1)/9} i, or ((10^n -1)/9)*((10^n -1)/9 +1)/2 (n-th term is the middle 2(n-1) digits of the (n+9)-th term for n > 1).
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%I #28 Feb 13 2023 03:22:02

%S 1,66,6216,617716,61732716,6172882716,617284382716,61728399382716,

%T 6172839549382716,617283951049382716,61728395066049382716,

%U 6172839506216049382716,617283950617716049382716,61728395061732716049382716,6172839506172882716049382716

%N Sum_{i=1..(10^n - 1)/9} i, or ((10^n -1)/9)*((10^n -1)/9 +1)/2 (n-th term is the middle 2(n-1) digits of the (n+9)-th term for n > 1).

%C Patterned, or almost palindromic, numbers obtained by modification of "half-repdigit" numbers. a[n]=A*(((100^n-1)/9)+B*(10^n - 1)/9)/18, where A=1, B=8-A=7. For example, n = 20: a[20] = 1111111111111111111188888888888888888888/18 = 61728395061728395066049382716049382716, an "almost-palindromic-number". - _Labos Elemer_, Oct 28 2004

%C n is "almost palindromic" if digitlist-Rev[digitlist], besides zeros, contains +1 or -1 in "regular" positions. - _Labos Elemer_, Oct 28 2004

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).

%F a(n) = A002275(n) * A093142(n).

%F G.f.: x*(-1+45*x) / ( (x-1)*(100*x-1)*(10*x-1) ). - _R. J. Mathar_, Mar 10 2011

%t f[x_] := 1*((100^x-1)/9) + 7*(10^x-1)/9 Table[f[w], {w, 1, 20}]/18 (* _Labos Elemer_, Oct 28 2004 *)

%o (PARI) Vec(x*(-1+45*x)/((x-1)*(100*x-1)*(10*x-1))+O(x^99)) \\ _Charles R Greathouse IV_, Jun 23 2020

%Y Cf. A002275, A093142, A098210, A099638.

%K nonn,base,easy

%O 1,2

%A Daniel Lawson (dlawson(AT)cats.ucsc.edu)

%E Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, May 31 2007