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 1-10 of 13 results. Next

A155662 a(n) = 11^n - 7^n + 1.

Original entry on oeis.org

1, 5, 73, 989, 12241, 144245, 1653913, 18663629, 208594081, 2317594085, 25654949353, 283334343869, 3124587089521, 34425823133525, 379071610510393, 4172500607905709, 45916496933002561, 505214397985306565, 5558288899894321033, 61147691553229173149
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 31 2009

Keywords

Links

Crossrefs

Cf. A155638, A155639, A155640, A155641, A155642, A155643, A155644, A155645, A155646, A155647, A155648, A155649, A155650, A155651, A155652, A155653, A155654, A155655, A155656, A155657, A155658, A155659, A155660, A155661.

Programs

Formula

G.f.: 1/(1-11*x) - 1/(1-7*x) + 1/(1-x).
E.g.f.: e^(11*x) - e^(7*x) + e^x.
a(n) = 18*a(n-1) - 77*a(n-2) + 60; a(0)=1, a(1)=5. - Vincenzo Librandi, Jul 21 2010

A155663 a(n) = 9^n + 8^n - 1.

Original entry on oeis.org

1, 16, 144, 1240, 10656, 91816, 793584, 6880120, 59823936, 521638216, 4560526224, 39970994200, 351149013216, 3091621642216, 27274838966064, 241075504183480, 2134495165562496, 18928981513351816, 168109033806481104, 1494966905748847960, 13310586963663775776
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.

Programs

  • Mathematica
    Table[9^n+8^n-1,{n,0,20}] (* or *) LinearRecurrence[{18,-89,72},{1,16,144},20] (* Harvey P. Dale, Jun 14 2016 *)
  • PARI
    a(n)=9^n+8^n-1 \\ Charles R Greathouse IV, Jun 11 2015

Formula

G.f.: 1/(1-9*x)+1/(1-8*x)-1/(1-x).
E.g.f.: exp(9*x)+exp(8*x)-exp(x).
a(n) = 17*a(n-1)-72*a(n-2)-56 with a(0) = 1, a(1) = 16. - Vincenzo Librandi, Jul 21 2010

A155664 a(n) = 10^n+8^n-1.

Original entry on oeis.org

1, 17, 163, 1511, 14095, 132767, 1262143, 12097151, 116777215, 1134217727, 11073741823, 108589934591, 1068719476735, 10549755813887, 104398046511103, 1035184372088831, 10281474976710655, 102251799813685247
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.

Programs

  • Mathematica
    Table[10^n+8^n-1,{n,0,20}] (* or *) LinearRecurrence[{19,-98,80},{1,17,163},20] (* Harvey P. Dale, Oct 11 2011 *)
  • PARI
    a(n)=10^n+8^n-1 \\ Charles R Greathouse IV, Jun 11 2015

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)=17. - Vincenzo Librandi, Jul 21 2010
a(0)=1, a(1)=17, a(2)=163, a(n)=19*a(n-1)-98*a(n-2)+80*a(n-3). - Harvey P. Dale, Oct 11 2011

A155665 a(n) = 11^n + 8^n - 1.

Original entry on oeis.org

1, 18, 184, 1842, 18736, 193818, 2033704, 21584322, 231136096, 2492165418, 27011166424, 293901605202, 3207147853456, 35072467957818, 384147880094344, 4212432541504482, 46231204840282816, 507698828312979018, 5577931712001713464, 61303205636490402162, 673902916437166856176
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.

Programs

  • Mathematica
    Table[11^n+8^n-1,{n,0,20}] (* or *) LinearRecurrence[{20,-107,88},{1,18,184},20] (* Harvey P. Dale, May 18 2011 *)
  • 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.: exp(11*x)+exp(8*x)-exp(x).
a(n) = 19*a(n-1)-88*a(n-2)-70 with a(0) = 1, a(1) = 18. - Vincenzo Librandi, Jul 21 2010
a(0) = 1, a(1) = 18, a(2) = 184, a(n) = 20*a(n-1)-107*a(n-2)+88*a(n-3). - Harvey P. Dale, May 18 2011

A155666 a(n) = 9^n - 8^n + 1.

Original entry on oeis.org

1, 2, 18, 218, 2466, 26282, 269298, 2685818, 26269506, 253202762, 2413042578, 22791125018, 213710059746, 1992110014442, 18478745943858, 170706760005818, 1571545212141186, 14425381885981322, 132080236787517138, 1206736529597136218, 11004743954450081826, 100195617094657583402
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.

Programs

Formula

G.f.: 1/(1-9*x)-1/(1-8*x)+1/(1-x).
E.g.f.: exp(9*x)-exp(8*x)+exp(x).
a(n) = 17*a(n-1)-72*a(n-2)+56 with a(0) = 1, a(1) = 2. - Vincenzo Librandi, Jul 21 2010

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
Showing 1-10 of 13 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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