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 1-6 of 6 results.

A147979 a(n) = 8^n-7^n-6^n-5^n-4^n-3^n-2^n-1.

Original entry on oeis.org

-6, -20, -76, -272, -580, 3760, 77324, 896848, 8869820, 81550960, 719926124, 6196609168, 52439953820, 438516694960, 3635082523724, 29935019892688, 245264010263420, 2001462391659760, 16280541150478124, 132087583623451408
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Nov 18 2008

Keywords

Links

Crossrefs

Cf. A147975, A147976, A147977, A147978.

Programs

  • Mathematica
    lst={};Do[p=8^n-7^n-6^n-5^n-4^n-3^n-2^n-1^n;AppendTo[lst,p],{n,0,5!}];lst
Table[8^n-Total[Range[7]^n],{n,0,20}] (* or *) LinearRecurrence[{36,-546,4536,-22449,67284,-118124,109584,-40320},{-6,-20,-76,-272,-580,3760,77324,896848},20] (* Harvey P. Dale, Nov 15 2014 *)
  • PARI
    a(n)=8^n-7^n-6^n-5^n-4^n-3^n-2^n-1 \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: 2*x*(49752*x^7-105056*x^6+87794*x^5-38129*x^4+9380*x^3-1316*x^2+98*x-3)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)*(8*x-1)). - Colin Barker, Oct 29 2012

A147976 a(n) = 5^n-4^n-3^n-2^n-1.

Original entry on oeis.org

-3, -5, -5, 25, 271, 1825, 10735, 59425, 318271, 1670785, 8656975, 44454625, 226827871, 1151991745, 5830280815, 29429454625, 148249811071, 745630312705, 3745590106255, 18797445635425, 94264432179871, 472428649241665
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Nov 18 2008

Keywords

Crossrefs

Cf. A147975-A147979.

Programs

  • Mathematica
    lst={};Do[p=5^n-4^n-3^n-2^n-1^n;AppendTo[lst,p],{n,0,5!}];lst
Table[5^n-4^n-3^n-2^n-1,{n,0,30}] (* Harvey P. Dale, Jul 27 2015 *)

Formula

G.f.: x*(3-40*x+185*x^2-350*x^3+226*x^4)/((x-1)*(4*x-1)*(3*x-1)*(2*x-1)*(5*x-1)). [Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009]

Extensions

G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.

A147977 a(n) = 6^n-5^n-4^n-3^n-2^n-1.

Original entry on oeis.org

-4, -9, -19, -9, 317, 3351, 26141, 183111, 1216637, 7842231, 49591901, 309595431, 1915328957, 11771279511, 71987413661, 438579282951, 2664183937277, 16146410851191, 97676152243421, 590010212989671, 3559688008961597
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Nov 18 2008

Keywords

Links

Crossrefs

Cf. A147975, A147976, A147978, A147979.

Programs

  • Mathematica
    lst={};Do[p=6^n-5^n-4^n-3^n-2^n-1^n;AppendTo[lst,p],{n,0,5!}];lst
Table[6^n-5^n-4^n-3^n-2^n-1,{n,0,20}] (* or *) LinearRecurrence[{21,-175,735,-1624,1764,-720},{-4,-9,-19,-9,317,3351},30] (* Harvey P. Dale, Jan 17 2017 *)

Formula

G.f.: x*(1524*x^5-2700*x^4+1755*x^3-530*x^2+75*x-4)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)). [Colin Barker, Oct 29 2012]

A147978 a(n) = 7^n-6^n-5^n-4^n-3^n-2^n-1.

Original entry on oeis.org

-5, -14, -42, -98, 126, 4606, 50478, 446782, 3622206, 28040446, 211134798, 1561328062, 11403051486, 82538901886, 593482158318, 4245770823742, 30254894691966, 214923605948926, 1522969836817038, 10770185918341822
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Nov 18 2008

Keywords

Links

Crossrefs

Cf. A147975, A147976, A147977, A147979.

Programs

  • Mathematica
    lst={};Do[p=7^n-6^n-5^n-4^n-3^n-2^n-1^n;AppendTo[lst,p],{n,0,5!}];lst

Formula

G.f.: x*(11628*x^6-22736*x^5+17059*x^4-6370*x^3+1260*x^2-126*x+5)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)). - Colin Barker, Oct 29 2012

A137786 a(n) = 4^n - 3^n - 2^n.

Original entry on oeis.org

-1, -1, 3, 29, 159, 749, 3303, 14069, 58719, 241949, 988503, 4015109, 16241679, 65506349, 263636103, 1059360149, 4251855039, 17050597949, 68331794103, 273715121189, 1096023794799, 4387584060749, 17560800790503, 70274592610229, 281192530396959, 1125052584678749
Offset: 0

Views

Author

Vladimir Joseph Stephan Orlovsky, Apr 28 2008

Keywords

Comments

a(n) mod 100 = 49 for n = 4*k + 1, k > 0; a(n) mod 100 = 3 for n = 4*k + 2, k >= 0. [Alex Ratushnyak, Jul 03 2012]

Links

Crossrefs

Cf. A001047, A005061, A074526, A083324, A147975.

Programs

  • Magma
    I:=[-1,-1,3]; [n le 3 select I[n] else 9*Self(n-1)-26*Self(n-2)+24*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Feb 12 2014
  • Maple
    A137786:=n->4^n - 3^n - 2^n; seq(A137786(n), n=0..25); # Wesley Ivan Hurt, Feb 10 2014
  • Mathematica
    Table[4^n - 3^n - 2^n, {n, 0, 25}] (* Bruno Berselli, Jul 04 2012 *)
LinearRecurrence[{9,-26,24},{-1,-1,3},30] (* Harvey P. Dale, Sep 19 2012 *)
CoefficientList[Series[-(1 - 8 x + 14 x^2)/((1 - 2 x) (1 - 3 x) (1 - 4 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 12 2014 *)
  • PARI
    a(n) = 4^n-3^n-2^n; \\ Joerg Arndt, Jul 04 2012
  • Python
    print([4**n - 3**n - 2**n for n in range(99)])
# Alex Ratushnyak, Jul 03 2012

Formula

G.f.: -(1-8*x+14*x^2)/((1-2*x)*(1-3*x)*(1-4*x)). - Bruno Berselli, Jul 04 2012
a(0)=-1, a(1)=-1, a(2)=3, a(n) = 9*a(n-1) - 26*a(n-2) + 24*a(n-3). - Harvey P. Dale, Sep 19 2012
E.g.f.: exp(2*x)*(exp(2*x) - exp(x) - 1). - Elmo R. Oliveira, Sep 12 2024

Extensions

Offset set to 0, terms corrected, more terms added by Alex Ratushnyak, Jul 03 2012.

A147996 a(n) = 9^n-8^n-7^n-6^n-5^n-4^n-3^n-2^n-1.

Original entry on oeis.org

-7, -27, -123, -567, -2211, -2727, 84477, 1485513, 18362109, 200535993, 2059226877, 20397799593, 197430536829, 1880870895513, 17715781956477, 165457407809673, 1535334245693949, 14175044463955833, 130346379428513277
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Nov 19 2008

Keywords

Links

Crossrefs

Cf. A147975-A147979.

Programs

  • Mathematica
    lst={};Do[p=9^n-8^n-7^n-6^n-5^n-4^n-3^n-2^n-1^n;AppendTo[lst,p],{n,0,5!}];lst

Formula

G.f.: x*(945936*x^8-2126232*x^7+1934792*x^6-942732*x^5+271467*x^4-47628*x^3+4998*x^2-288*x+7)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)*(8*x-1)*(9*x-1)). - Colin Barker, Oct 29 2012
Showing 1-6 of 6 results.

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