A003555 - OEIS

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).

1, 66, 6216, 617716, 61732716, 6172882716, 617284382716, 61728399382716, 6172839549382716, 617283951049382716, 61728395066049382716, 6172839506216049382716, 617283950617716049382716, 61728395061732716049382716, 6172839506172882716049382716

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OFFSET

1,2

COMMENTS

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

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

LINKS

Table of n, a(n) for n=1..15.

Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

FORMULA

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

G.f.: x*(-1+45*x) / ( (x-1)*(100*x-1)*(10*x-1) ). - R. J. Mathar, Mar 10 2011

MATHEMATICA

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

PROG

(PARI) Vec(x*(-1+45*x)/((x-1)*(100*x-1)*(10*x-1))+O(x^99)) \\ Charles R Greathouse IV, Jun 23 2020

CROSSREFS