cp's OEIS Frontend

A003555 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).

%I A003555 #28 Feb 13 2023 03:22:02
%S A003555 1,66,6216,617716,61732716,6172882716,617284382716,61728399382716,
%T A003555 6172839549382716,617283951049382716,61728395066049382716,
%U A003555 6172839506216049382716,617283950617716049382716,61728395061732716049382716,6172839506172882716049382716
%N A003555 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 A003555 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 A003555 n is "almost palindromic" if digitlist-Rev[digitlist], besides zeros, contains +1 or -1 in "regular" positions. - _Labos Elemer_, Oct 28 2004
%H A003555 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A003555 a(n) = A002275(n) * A093142(n).
%F A003555 G.f.: x*(-1+45*x) / ( (x-1)*(100*x-1)*(10*x-1) ). - _R. J. Mathar_, Mar 10 2011
%t A003555 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 A003555 (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 A003555 Cf. A002275, A093142, A098210, A099638.
%K A003555 nonn,base,easy
%O A003555 1,2
%A A003555 Daniel Lawson (dlawson(AT)cats.ucsc.edu)
%E A003555 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, May 31 2007