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 12 results. Next

A189732 a(1)=1, a(2)=5, a(n) = a(n-1) + 5*a(n-2).

Original entry on oeis.org

1, 5, 10, 35, 85, 260, 685, 1985, 5410, 15335, 42385, 119060, 330985, 926285, 2581210, 7212635, 20118685, 56181860, 156775285, 437684585, 1221561010, 3409983935, 9517788985, 26567708660, 74156653585, 206995196885, 577778464810, 1612754449235, 4501646773285
Offset: 1

Views

Author

Harvey P. Dale, Apr 26 2011

Keywords

Links

Crossrefs

Cf. A000045, A000079, A105476, A159612, A080040, A135522, A103435, A189734, A189735, A189736, A189737, A189738, A189739, A189741, A189742, A189743, A189744, A189745, A189746, A189747, A189748, A189749.

Programs

  • Mathematica
    LinearRecurrence[{1,5},{1,5},40]
  • Maxima
    a[1]:1$ a[2]:5$ a[n]:=a[n-1]+5*a[n-2]$ makelist(a[n], n, 1, 29);  /* Bruno Berselli, May 24 2011 */
  • PARI
    a(n)=([0,1; 5,1]^(n-1)*[1;5])[1,1] \\ Charles R Greathouse IV, Oct 21 2022

Formula

G.f.: x*(1+4*x)/(1-x-5*x^2). - Bruno Berselli, May 24 2011
a(n+1) = Sum_{k=0..n} A119473(n,k)*4^k. - Philippe Deléham, Oct 05 2012

A189741 a(1)=4, a(2)=2, a(n) = 4*a(n-1) + 2*a(n-2).

Original entry on oeis.org

4, 2, 16, 68, 304, 1352, 6016, 26768, 119104, 529952, 2358016, 10491968, 46683904, 207719552, 924246016, 4112423168, 18298184704, 81417585152, 362266710016, 1611902010368, 7172141461504, 31912369866752, 141993762390016, 631799789293568, 2811186681954304
Offset: 1

Views

Author

Harvey P. Dale, Apr 26 2011

Keywords

Links

Crossrefs

Cf. A000045, A000079, A105476, A159612, A080040, A135522, A103435, A189732, A189734, A189735, A189736, A189737, A189738, A189739, A189742, A189743, A189744, A189745, A189746, A189747, A189748, A189749.

Programs

  • Mathematica
    LinearRecurrence[{4,2},{4,2},40]
  • Maxima
    a[1]:4$ a[2]:2$ a[n]:=4*a[n-1]+2*a[n-2]$ makelist(a[n], n, 1, 25);  /* Bruno Berselli, May 24 2011 */

Formula

G.f.: 2*x*(2-7*x)/(1-4*x-2*x^2). - Bruno Berselli, May 24 2011

A189736 a(1)=3, a(2)=2, a(n)=3*a(n-1) + 2*a(n-2).

Original entry on oeis.org

3, 2, 12, 40, 144, 512, 1824, 6496, 23136, 82400, 293472, 1045216, 3722592, 13258208, 47219808, 168175840, 598967136, 2133253088, 7597693536, 27059586784, 96374147424, 343241615840, 1222473142368, 4353902658784, 15506654261088, 55227768100832
Offset: 1

Views

Author

Harvey P. Dale, Apr 26 2011

Keywords

Links

Crossrefs

Cf. A000045, A000079, A105476, A159612, A080040, A135522, A103435, A189732, A189734, A189735, A189737, A189738, A189739, A189741, A189742, A189743, A189744, A189745, A189746, A189747, A189748, A189749.

Programs

  • Mathematica
    LinearRecurrence[{3,2},{3,2},40]
  • Maxima
    a[1]:3$ a[2]:2$ a[n]:=3*a[n-1]+2*a[n-2]$ makelist(a[n], n, 1, 26); /* Bruno Berselli, May 24 2011 */

Formula

G.f.: x*(3-7*x)/(1-3*x-2*x^2). - Bruno Berselli, May 24 2011

A189742 a(1)=4, a(2)=3, a(n) = 4*a(n-1) + 3*a(n-2).

Original entry on oeis.org

4, 3, 24, 105, 492, 2283, 10608, 49281, 228948, 1063635, 4941384, 22956441, 106649916, 495468987, 2301825696, 10693709745, 49680316068, 230802393507, 1072250522232, 4981409269449, 23142388644492, 107513782386315, 499482295478736, 2320470529073889
Offset: 1

Views

Author

Harvey P. Dale, Apr 26 2011

Keywords

Links

Crossrefs

Cf. A000045, A000079, A105476, A159612, A080040, A135522, A103435, A189732, A189734, A189735, A189736, A189737, A189738, A189739, A189741, A189743, A189744, A189745, A189746, A189747, A189748, A189749.

Programs

  • Mathematica
    LinearRecurrence[{4,3},{4,3},40]
  • Maxima
    a[1]:4$ a[2]:3$ a[n]:=4*a[n-1]+3*a[n-2]$ makelist(a[n], n, 1, 24); /* Bruno Berselli, May 24 2011 */

Formula

G.f.: x*(4-13*x)/(1-4*x-3*x^2). - Bruno Berselli, May 24 2011

A189743 a(1)=4, a(2)=4, a(n) = 4*a(n-1) + 4*a(n-2).

Original entry on oeis.org

4, 4, 32, 144, 704, 3392, 16384, 79104, 381952, 1844224, 8904704, 42995712, 207601664, 1002389504, 4839964672, 23369416704, 112837525504, 544827768832, 2630661177344, 12701955784704, 61330467848192, 296129694531584, 1429840649519104, 6903881376202752
Offset: 1

Views

Author

Harvey P. Dale, Apr 26 2011

Keywords

Links

Crossrefs

Cf. A000045, A000079, A105476, A159612, A080040, A135522, A103435, A189732, A189734, A189735, A189736, A189737, A189738, A189739, A189741, A189742, A189744, A189745, A189746, A189747, A189748, A189749.

Programs

  • Mathematica
    LinearRecurrence[{4,4},{4,4},40]
  • Maxima
    a[1]:4$ a[2]:4$ a[n]:=4*a[n-1]+4*a[n-2]$ makelist(a[n], n, 1, 24); /* Bruno Berselli, May 24 2011 */

Formula

G.f.: 4*x*(1-3*x)/(1-4*x-4*x^2). - Bruno Berselli, May 24 2011

A189744 a(1)=4, a(2)=5, a(n) = 4*a(n-1) + 5*a(n-2).

Original entry on oeis.org

4, 5, 40, 185, 940, 4685, 23440, 117185, 585940, 2929685, 14648440, 73242185, 366210940, 1831054685, 9155273440, 45776367185, 228881835940, 1144409179685, 5722045898440, 28610229492185, 143051147460940, 715255737304685, 3576278686523440, 17881393432617185
Offset: 1

Views

Author

Harvey P. Dale, Apr 26 2011

Keywords

Links

Crossrefs

Cf. A000045, A000079, A105476, A159612, A080040, A135522, A103435, A189732, A189734-A189739, A189741, A189742, A189743, A189745-A189749.

Programs

  • Magma
    [5/2*(-1)^(n-1)+3/2*5^(n-1): n in [1..30]]; // Vincenzo Librandi, Jul 15 2011
  • Mathematica
    LinearRecurrence[{4,5},{4,5},40]
  • Maxima
    a[1]:4$ a[2]:5$ a[n]:=4*a[n-1]+5*a[n-2]$ makelist(a[n], n, 1, 24); /* Bruno Berselli, May 24 2011 */
  • PARI
    a(n)=5/2*(-1)^(n-1)+3/2*5^(n-1) \\ Charles R Greathouse IV, Jul 02 2013

Formula

G.f.: x*(4-11*x)/(1 - 4*x - 5*x^2). - Bruno Berselli, May 24 2011

A189745 a(n) = 5*a(n-1) + a(n-2); with a(1)=5, a(2)=1.

Original entry on oeis.org

5, 1, 10, 51, 265, 1376, 7145, 37101, 192650, 1000351, 5194405, 26972376, 140056285, 727253801, 3776325290, 19608880251, 101820726545, 528712512976, 2745383291425, 14255628970101, 74023528141930, 384373269679751, 1995889876540685, 10363822652383176
Offset: 1

Views

Author

Harvey P. Dale, Apr 26 2011

Keywords

Links

Crossrefs

Cf. A000045, A000079, A105476, A159612, A080040, A135522, A103435, A189732, A189734, A189735, A189736, A189737, A189738, A189739, A189741, A189742, A189743, A189744, A189746, A189747, A189748, A189749.

Programs

  • Mathematica
    LinearRecurrence[{5,1},{5,1},40]
  • Maxima
    a[1]:5$ a[2]:1$ a[n]:=5*a[n-1]+a[n-2]$ makelist(a[n], n, 1, 24); /*
 Bruno Berselli, May 24 2011 */

Formula

G.f.: x*(5-24*x)/(1-5*x-x^2). - Bruno Berselli, May 24 2011

A189749 a(1)=5, a(2)=5, a(n)=5*a(n-1) + 5*a(n-2).

Original entry on oeis.org

5, 5, 50, 275, 1625, 9500, 55625, 325625, 1906250, 11159375, 65328125, 382437500, 2238828125, 13106328125, 76725781250, 449160546875, 2629431640625, 15392960937500, 90111962890625, 527524619140625, 3088182910156250, 18078537646484375, 105833602783203125
Offset: 1

Views

Author

Harvey P. Dale, Apr 26 2011

Keywords

Links

Crossrefs

Cf. A000045, A000079, A105476, A159612, A080040, A135522, A103435, A189732, A189734, A189735, A189736, A189737, A189738, A189739, A189741, A189742, A189743, A189744, A189745, A189746, A189747, A189748.

Programs

  • Mathematica
    LinearRecurrence[{5,5},{5,5},40]
  • Maxima
    a[1]:5$ a[2]:5$ a[n]:=5*a[n-1]+5*a[n-2]$ makelist(a[n], n, 1, 23); /* Bruno Berselli, May 24 2011 */

Formula

G.f.: 5*x*(1-4*x)/(1-5*x-5*x^2). - Bruno Berselli, May 24 2011
a(n) = 5*A188168(n). - R. J. Mathar, Feb 13 2020

A189737 a(1)=3, a(2)=3, a(n)=3*a(n-1) + 3*a(n-2).

Original entry on oeis.org

3, 3, 18, 63, 243, 918, 3483, 13203, 50058, 189783, 719523, 2727918, 10342323, 39210723, 148659138, 563609583, 2136806163, 8101247238, 30714160203, 116446222323, 441481147578, 1673782109703, 6345789771843, 24058715644638, 91213516249443, 345816695682243
Offset: 1

Views

Author

Harvey P. Dale, Apr 26 2011

Keywords

Links

Crossrefs

Cf. A000045, A000079, A105476, A159612, A080040, A135522, A103435, A189732, A189734, A189735, A189736, A189738, A189739, A189741, A189742, A189743, A189744, A189745, A189746, A189747, A189748, A189749.

Programs

  • Mathematica
    LinearRecurrence[{3,3},{3,3},40]
  • Maxima
    a[1]:3$ a[2]:3$ a[n]:=3*a[n-1]+3*a[n-2]$ makelist(a[n], n, 1, 26); /* Bruno Berselli, May 24 2011 */

Formula

G.f.: 3*x*(1-2*x)/(1-3*x-3*x^2). - Bruno Berselli, May 24 2011

A189746 a(1)=5, a(2)=2, a(n) = 5*a(n-1) + 2*a(n-2).

Original entry on oeis.org

5, 2, 20, 104, 560, 3008, 16160, 86816, 466400, 2505632, 13460960, 72316064, 388502240, 2087143328, 11212721120, 60237892256, 323614903520, 1738550302112, 9339981317600, 50177007192224, 269564998596320, 1448179007366048, 7780025034022880, 41796483184846496
Offset: 1

Views

Author

Harvey P. Dale, Apr 26 2011

Keywords

Links

Crossrefs

Cf. A000045, A000079, A105476, A159612, A080040, A135522, A103435, A189732, A189734, A189735, A189736, A189737, A189738, A189739, A189741, A189742, A189743, A189744, A189745, A189747, A189748, A189749.

Programs

  • Mathematica
    LinearRecurrence[{5,2},{5,2},40]
  • Maxima
    a[1]:5$ a[2]:2$ a[n]:=5*a[n-1]+2*a[n-2]$ makelist(a[n], n, 1, 24); /* Bruno Berselli, May 24 2011 */

Formula

G.f.: x*(5-23*x)/(1-5*x-2*x^2). - Bruno Berselli, May 24 2011
Showing 1-10 of 12 results. Next

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

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