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.

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A128787 n^2*8^n.

Original entry on oeis.org

0, 8, 256, 4608, 65536, 819200, 9437184, 102760448, 1073741824, 10871635968, 107374182400, 1039382085632, 9895604649984, 92908732547072, 862017116176384, 7916483719987200, 72057594037927936, 650770146155036672
Offset: 0

Views

Author

Mohammad K. Azarian, Apr 07 2007

Keywords

Comments

Subsequence of A047351. [Bruno Berselli, Feb 07 2013]

Examples

			a(1) = 1^2 * 8^1 = 1 * 8 = 8.
a(2) = 2^2 * 8^2 = 4 * 64 = 256.
a(3) = 3^2 * 8^3 = 9 * 512 = 4608.

Links

Crossrefs

Cf. A036289, A007758.

Programs

  • Magma
    [n^2*8^n: n in [0..20]]; // Vincenzo Librandi, Feb 06 2013
  • Mathematica
    LinearRecurrence[{24, -192, 512}, {0, 8, 256}, 30] (* or *) CoefficientList[Series[8 x (1 + 8 x)/((1 - 8 x)^3), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 06 2013 *)
Table[n^2 8^n, {n, 0, 19}] (* Alonso del Arte, Feb 06 2013 *)

Formula

G.f.: 8*x*(1 + 8*x)/(1 - 8*x)^3. - Vincenzo Librandi, Feb 06 2013
a(n) = 24*a(n-1) - 192*a(n-2) + 512*a(n-3). - Vincenzo Librandi, Feb 06 2013

A128788 a(n) = n^2*9^n.

Original entry on oeis.org

0, 9, 324, 6561, 104976, 1476225, 19131876, 234365481, 2754990144, 31381059609, 348678440100, 3797108212689, 40669853253264, 429575324987601, 4483851321172356, 46325504721296025, 474373168346071296
Offset: 0

Views

Author

Mohammad K. Azarian, Apr 07 2007

Keywords

Comments

Subsequence of A008854 and A047462. [Bruno Berselli, Feb 07 2013]

Links

Crossrefs

Cf. A007758, A008854, A036289, A047462.

Programs

  • Magma
    [n^2*9^n: n in [0..20]]; // Vincenzo Librandi, Feb 07 2013
  • Mathematica
    CoefficientList[Series[9 x (1 + 9 x)/(1 - 9 x)^3, {x, 0, 30}], x] (* or *) LinearRecurrence[{27, -243, 729}, {0, 9, 324}, 20] (* Vincenzo Librandi, Feb 07 2013 *)

Formula

G.f.: 9*x*(1+9*x)/(1-9*x)^3. - Vincenzo Librandi, Feb 07 2013
a(n) = 27*a(n-1) - 243*a(n-2) + 729*a(n-3). - Vincenzo Librandi, Feb 07 2013

A128790 n^3*4^n.

Original entry on oeis.org

0, 4, 128, 1728, 16384, 128000, 884736, 5619712, 33554432, 191102976, 1048576000, 5582618624, 28991029248, 147438174208, 736586891264, 3623878656000, 17592186044416, 84404697300992, 400771988324352, 1885387563728896
Offset: 0

Views

Author

Mohammad K. Azarian, Apr 07 2007

Keywords

Comments

All terms are congruent to {0, 2, 4} mod 6 (or mod 9 or mod 18). [Bruno Berselli, Feb 07 2013]

Links

Crossrefs

Cf. A036289; A007758.

Programs

  • Magma
    [n^3*4^n: n in [0..30]]; // Vincenzo Librandi, Feb 07 2013
  • Mathematica
    CoefficientList[Series[4*x*(1 + 16*x + 16*x^2)/(1 - 4*x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 07 2013 *)
Table[n^3 4^n,{n,0,20}] (* or *) LinearRecurrence[{16,-96,256,-256},{0,4,128,1728},20] (* Harvey P. Dale, Nov 24 2022 *)

Formula

G.f.: 4*x*(1 + 16*x + 16*x^2)/(1 - 4*x)^4. - Vincenzo Librandi, Feb 07 2013

A128791 a(n) = n^3 * 5^n.

Original entry on oeis.org

0, 5, 200, 3375, 40000, 390625, 3375000, 26796875, 200000000, 1423828125, 9765625000, 64990234375, 421875000000, 2681884765625, 16748046875000, 102996826171875, 625000000000000, 3748321533203125, 22247314453125000
Offset: 0

Views

Author

Mohammad K. Azarian, Apr 07 2007

Keywords

Comments

Subsequence of A047486. [Bruno Berselli, Feb 07 2013]

Links

Crossrefs

Cf. A036289, A007758.

Programs

  • Magma
    [n^3*5^n: n in [0..30]]; // Vincenzo Librandi, Feb 07 2013
  • Magma
    I:=[0, 5, 200, 3375]; [n le 4 select I[n] else 20*Self(n-1)-150*Self(n-2)+500*Self(n-3)-625*Self(n-4): n in [1..30]]; // Vincenzo Librandi, Feb 09 2013
  • Mathematica
    CoefficientList[Series[5 x (1 + 20 x + 25 x^2)/(1-5 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 07 2013 *)
LinearRecurrence[{20,-150,500,-625},{0,5,200,3375},20] (* Harvey P. Dale, Aug 16 2024 *)

Formula

G.f.: 5*x*(1+20*x+25*x^2)/(1-5*x)^4. - Vincenzo Librandi Feb 07 2013
a(n) = 20*a(n-1) - 150*a(n-2) + 500*a(n-3) - 625*a(n-4). - Vincenzo Librandi, Feb 09 2013

A128792 n^3*6^n.

Original entry on oeis.org

0, 6, 288, 5832, 82944, 972000, 10077696, 96018048, 859963392, 7346640384, 60466176000, 482882881536, 3761479876608, 28694344753152, 215031266279424, 1586874322944000, 11555266180939776, 83160677851987968
Offset: 0

Views

Author

Mohammad K. Azarian, Apr 07 2007

Keywords

Links

Crossrefs

Cf. A036289, A007758.

Programs

  • Magma
    [n^3*6^n: n in [0..20]]; // Vincenzo Librandi, Feb 08 2013
  • Magma
    I:=[0, 6, 288, 5832]; [n le 4 select I[n] else 24*Self(n-1)-216*Self(n-2)+864*Self(n-3)-1296*Self(n-4): n in [1..30]]; // Vincenzo Librandi, Feb 09 2013
  • Mathematica
    CoefficientList[Series[6 x *(1+24 x + 36 x^2)/(1-6*x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 08 2013 *)
LinearRecurrence[{24,-216,864,-1296},{0,6,288,5832},20] (* Harvey P. Dale, Mar 12 2023 *)

Formula

G.f.: 6*x*(1 + 24*x + 36*x^2)/(1 - 6*x)^4. - Vincenzo Librandi, Feb 08 2013
a(n) = 24*a(n-1) - 216*a(n-2) + 864*a(n-3) - 1296*a(n-4). - Vincenzo Librandi, Feb 09 2013

A128793 n^3*7^n.

Original entry on oeis.org

0, 7, 392, 9261, 153664, 2100875, 25412184, 282475249, 2951578112, 29417779503, 282475249000, 2631821894933, 23917744283328, 212865155864179, 1861044111897656, 16023020096057625, 136122083613085696
Offset: 0

Views

Author

Mohammad K. Azarian, Apr 07 2007

Keywords

Links

Crossrefs

Cf. A036289, A007758.

Programs

  • Magma
    [n^3*7^n: n in [0..20]]; // Vincenzo Librandi, Feb 08 2013
  • Magma
    I:=[0,7,392,9261]; [n le 4 select I[n] else 28*Self(n-1)-294*Self(n-2)+1372*Self(n-3)-2401*Self(n-4): n in [1..30]]; // Vincenzo Librandi, Feb 09 2013
  • Mathematica
    CoefficientList[Series[7*x*(1 + 28*x + 49*x^2)/(1 - 7*x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Feb 08 2013 *)
Table[n^3 7^n,{n,0,20}] (* or *) LinearRecurrence[{28,-294,1372,-2401},{0,7,392,9261},20] (* Harvey P. Dale, Aug 30 2020 *)

Formula

G.f.: 7*x*(1 + 28*x + 49x^2)/(1 - 7*x)^4. - Vincenzo Librandi, Feb 08 2013
a(n) = 28*a(n-1) - 294*a(n-2) + 1372*a(n-3) - 2401*a(n-4). - Vincenzo Librandi, Feb 09 2013

A128794 n^3*8^n.

Original entry on oeis.org

0, 8, 512, 13824, 262144, 4096000, 56623104, 719323136, 8589934592, 97844723712, 1073741824000, 11433202941952, 118747255799808, 1207813523111936, 12068239626469376, 118747255799808000, 1152921504606846976
Offset: 0

Views

Author

Mohammad K. Azarian, Apr 07 2007

Keywords

Links

Crossrefs

Cf. A036289, A007758.

Programs

  • Magma
    [n^3*8^n: n in [0..20]]; // Vincenzo Librandi, Feb 10 2013
  • Mathematica
    CoefficientList[Series[8 x (1 + 32 x + 64 x^2)/(1 - 8 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 10 2013 *)

Formula

G.f.: 8*x*(1 + 32*x + 64*x^2)/(1 - 8*x)^4. - Vincenzo Librandi, Feb 10 2013
a(n) = 32*a(n-1) -384*a(n-2) +2048*a(n-3) -4096*a(n-4). - Vincenzo Librandi, Feb 10 2013

A128795 n^3*9^n.

Original entry on oeis.org

0, 9, 648, 19683, 419904, 7381125, 114791256, 1640558367, 22039921152, 282429536481, 3486784401000, 41768190339579, 488038239039168, 5584479224838813, 62773918496412984, 694882570819440375
Offset: 0

Views

Author

Mohammad K. Azarian, Apr 07 2007

Keywords

Links

Crossrefs

Cf. A036289, A007758.

Programs

  • Magma
    [n^3*9^n: n in [0..20]]; // Vincenzo Librandi, Feb 10 2013
  • Mathematica
    CoefficientList[Series[9 x (1 + 36 x + 81 x^2)/(1 - 9 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 10 2013 *)

Formula

G.f.: 9*x*(1+36*x+81*x^2)/(1-9*x)^4. [R. J. Mathar, Dec 19 2008]
a(n) = 36*a(n-1) -486*a(n-2) +2916*a(n-3) -6561*a(n-4). - Vincenzo Librandi, Feb 10 2013

A128797 (n^2-n)*3^n.

Original entry on oeis.org

0, 0, 18, 162, 972, 4860, 21870, 91854, 367416, 1417176, 5314410, 19486170, 70150212, 248714388, 870500358, 3013270470, 10331213040, 35126124336, 118550669634, 397493421714, 1324978072380, 4393348345260, 14498049539358
Offset: 0

Views

Author

Mohammad K. Azarian, Apr 07 2007

Keywords

Links

Crossrefs

Cf. A036289, A007758.

Programs

  • Magma
    [(n^2-n)*3^n: n in [0..25]]; // Vincenzo Librandi, Feb 10 2013
  • Mathematica
    CoefficientList[Series[18 x^2/(1 - 3 x)^3, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 10 2013 *)
LinearRecurrence[{9,-27,27},{0,0,18},40] (* Harvey P. Dale, Dec 15 2014 *)

Formula

G.f.: 18*x^2/(1-3*x)^3. - Vincenzo Librandi, Feb 10 2013
a(n) = 18*A027472(n+1). - R. J. Mathar, Apr 26 2015

A128798 n*(n-1)*4^n.

Original entry on oeis.org

0, 0, 32, 384, 3072, 20480, 122880, 688128, 3670016, 18874368, 94371840, 461373440, 2214592512, 10468982784, 48855252992, 225485783040, 1030792151040, 4672924418048, 21028159881216, 94008244174848, 417814418554880
Offset: 0

Views

Author

Mohammad K. Azarian, Apr 07 2007

Keywords

Links

Crossrefs

Cf. A036289, A007758.

Programs

  • Magma
    [(n^2-n)*4^n: n in [0..20]]; // Vincenzo Librandi, Feb 10 2013
  • Mathematica
    CoefficientList[Series[32 x^2/(1 - 4 x)^3, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 10 2013 *)
LinearRecurrence[{12,-48,64},{0,0,32},30] (* Harvey P. Dale, Dec 23 2015 *)

Formula

G.f.: 32*x^2/(1 - 4*x)^3. - Vincenzo Librandi, Feb 10 2013
a(n) =32*A038845(n-2). - R. J. Mathar, Apr 26 2015
Previous Showing 31-40 of 49 results. Next

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

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