cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-8 of 8 results.

A155667 a(n) = 10^n-8^n+1.

Original entry on oeis.org

1, 3, 37, 489, 5905, 67233, 737857, 7902849, 83222785, 865782273, 8926258177, 91410065409, 931280523265, 9450244186113, 95601953488897, 964815627911169, 9718525023289345, 97748200186314753, 981985601490518017
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 31 2009

Keywords

Links

Crossrefs

Cf. A155646, A155647, A155648, A155649, A155650, A155651, A155652, A155653, A155654, A155655, A155656, A155657, A155658, A155659, A155660, A155661, A155662, A155663, A155664, A155665, A155666.

Programs

Formula

G.f.: 1/(1-10*x)-1/(1-8*x)+1/(1-x).
E.g.f.: e^(10*x)-e^(8*x)+e^x.
a(n) = 18*a(n-1)-80*a(n-2)+63 with a(0) = 1, a(1) = 3. - Vincenzo Librandi, Jul 21 2010
a(n) = 19*a(n-1) - 98*a(n-2) + 80*a(n-3). - Wesley Ivan Hurt, Apr 18 2023

A155668 11^n-8^n+1.

Original entry on oeis.org

1, 4, 58, 820, 10546, 128284, 1509418, 17390020, 197581666, 2223729964, 24863682778, 276721736020, 3069708899986, 33972956330044, 375351787072138, 4142063797326820, 45668254886861506, 503195228685608524
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 31 2009

Keywords

Links

Crossrefs

Cf. A155646, A155647, A155648, A155649, A155650, A155651, A155652, A155653, A155654, A155655, A155656, A155657, A155658, A155659, A155660, A155661, A155662, A155663, A155664, A155665, A155666, A155667.

Programs

  • Mathematica
    Table[11^n-8^n+1,{n,0,20}] (* or *) LinearRecurrence[{20,-107,88},{1,4,58},20] (* Harvey P. Dale, Jan 12 2019 *)
  • PARI
    a(n)=11^n-8^n+1 \\ Charles R Greathouse IV, Jun 11 2015

Formula

G.f.: 1/(1-11*x)-1/(1-8*x)+1/(1-x). E.g.f.: e^(11*x)-e^(8*x)+e^x.
a(n)=19*a(n-1)-88*a(n-2)+70 with a(0)=1, a(1)=4 - Vincenzo Librandi, Jul 21 2010

A155669 10^n+9^n-1.

Original entry on oeis.org

1, 18, 180, 1728, 16560, 159048, 1531440, 14782968, 143046720, 1387420488, 13486784400, 131381059608, 1282429536480, 12541865828328, 122876792454960, 1205891132094648, 11853020188851840, 116677181699666568
Offset: 0

Views

Author

Mohammad K. Azarian, Feb 01 2009

Keywords

Links

Crossrefs

Cf. A155646, A155647, A155648, A155649, A155650, A155651, A155652, A155653, A155654, A155655, A155656, A155657, A155658, A155659, A155660, A155661, A155662, A155663, A155664, A155665, A155666, A155667, A155668.

Programs

Formula

G.f.: 1/(1-10*x)+1/(1-9*x)-1/(1-x). E.g.f.: e^(10*x)+e^(9*x)-e^x.
a(n)=19*a(n-1)-90*a(n-2)-72 with a(0)=1, a(1)=18 - Vincenzo Librandi, Jul 21 2010

A155670 11^n+9^n-1^n.

Original entry on oeis.org

1, 19, 201, 2059, 21201, 220099, 2303001, 24270139, 257405601, 2745368179, 29424209001, 316692730219, 3420857913201, 37064577972259, 402626626038201, 4383139301510299, 47802750052424001, 522124210198960339
Offset: 0

Views

Author

Mohammad K. Azarian, Feb 01 2009

Keywords

Links

Crossrefs

A155646, A155647, A155648, A155649, A155650, A155651, A155652, A155653, A155654, A155655, A155656, A155657, A155658, A155659, A155660, A155661, A155662, A155663, A155664, A155665, A155666, A155667, A155668, A155669

Programs

Formula

G.f.: 1/(1-11*x)+1/(1-9*x)-1/(1-x). E.g.f.: e^(11*x)+e^(9*x)-e^x.
a(n)=20*a(n-1)-99*a(n-2)-80 with a(0)=1, a(1)=19 - Vincenzo Librandi, Jul 21 2010

A155671 a(n) = 10^n - 9^n + 1^n.

Original entry on oeis.org

1, 2, 20, 272, 3440, 40952, 468560, 5217032, 56953280, 612579512, 6513215600, 68618940392, 717570463520, 7458134171672, 77123207545040, 794108867905352, 8146979811148160, 83322818300333432, 849905364703000880
Offset: 0

Views

Author

Mohammad K. Azarian, Feb 01 2009

Keywords

Comments

a(n) is the number of numbers from 1 to 10^n containing a 1 in their decimal expansion. - Charles R Greathouse IV, Mar 25 2009

Links

Crossrefs

Equals A016189 + 1. See that entry for more information.
Cf. A155654, A155655, A155656, A155657, A155658, A155659, A155660, A155661, A155662, A155663, A155664, A155665, A155666, A155667, A155668, A155669, A155670.

Programs

Formula

G.f.: 1/(1-10*x)-1/(1-9*x)+1/(1-x).
E.g.f.: e^(10*x)-e^(9*x)+e^x.
a(n) = 19*a(n-1)-90*a(n-2)+72 with a(0)=1, a(1)=2. - Vincenzo Librandi, Jul 21 2010
a(n) = 20*a(n-1)-109*a(n-2)+90*a(n-3). - Wesley Ivan Hurt, Apr 21 2021

A155672 11^n-9^n+1^n.

Original entry on oeis.org

1, 3, 41, 603, 8081, 102003, 1240121, 14704203, 171312161, 1970527203, 22450640201, 253930611003, 2855998840241, 31980846315603, 356873041128281, 3971357037321003, 44096709674720321, 488769846799627203
Offset: 0

Views

Author

Mohammad K. Azarian, Feb 01 2009

Keywords

Links

Crossrefs

A155654, A155655, A155656, A155657, A155658, A155659, A155660, A155661, A155662, A155663, A155664, A155665, A155666, A155667, A155668, A155669, A155670, A155671

Programs

  • Mathematica
    Table[11^n-9^n+1,{n,0,30}] (* or *) LinearRecurrence[{21,-119,99},{1,3,41},30] (* Harvey P. Dale, May 07 2019 *)

Formula

G.f.: 1/(1-11*x)-1/(1-9*x)+1/(1-x). E.g.f.: e^(11*x)-e^(9*x)+e^x.
a(n)=20*a(n-1)-99*a(n-2)+80 with a(0)=1, a(1)=3 [From Vincenzo Librandi, Jul 21 2010]

A155673 a(n) = 11^n + 10^n - 1.

Original entry on oeis.org

1, 20, 220, 2330, 24640, 261050, 2771560, 29487170, 314358880, 3357947690, 35937424600, 385311670610, 4138428376720, 44522712143930, 479749833583240, 5177248169415650, 55949729863572160, 605447028499293770
Offset: 0

Views

Author

Mohammad K. Azarian, Feb 01 2009

Keywords

Links

Crossrefs

Cf. A155654, A155655, A155656, A155657, A155658, A155659, A155660, A155661, A155662, A155663, A155664, A155665, A155666, A155667, A155668, A155669, A155670, A155671, A155672.

Programs

  • Mathematica
    Table[11^n+10^n-1,{n,0,20}] (* Harvey P. Dale, Feb 24 2011 *)

Formula

G.f.: 1/(1-11*x)+1/(1-10*x)-1/(1-x).
E.g.f.: e^(11*x)+e^(10*x)-e^x.
a(n) = 21*a(n-1)-110*a(n-2)-90 with a(0)=1, a(1)=20. - Vincenzo Librandi, Jul 21 2010
a(n) = 22*a(n-1)-131*a(n-2)+110*a(n-3). - Wesley Ivan Hurt, May 19 2024

A155674 11^n-10^n+1^n.

Original entry on oeis.org

1, 2, 22, 332, 4642, 61052, 771562, 9487172, 114358882, 1357947692, 15937424602, 185311670612, 2138428376722, 24522712143932, 279749833583242, 3177248169415652, 35949729863572162, 405447028499293772
Offset: 0

Views

Author

Mohammad K. Azarian, Feb 01 2009

Keywords

Links

Crossrefs

A155654, A155655, A155656, A155657, A155658, A155659, A155660, A155661, A155662, A155663, A155664, A155665, A155666, A155667, A155668, A155669, A155670, A155671, A155672, A155673

Formula

G.f.: 1/(1-11*x)-1/(1-10*x)+1/(1-x). E.g.f.: e^(11*x)-e^(10*x)+e^x.
a(n)=21*a(n-1)-110*a(n-2)+90 with a(0)=1, a(1)=2 [From Vincenzo Librandi, Jul 21 2010]
Showing 1-8 of 8 results.

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