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.

A135168 a(n) = 7^n + 5^n + 3^n + 2^n.

Original entry on oeis.org

4, 17, 87, 503, 3123, 20207, 134067, 903983, 6162243, 42326927, 292300947, 2026334063, 14085963363, 98111316047, 684331387827, 4778093469743, 33385561572483, 233393582711567, 1632228682858707, 11417969834487023, 79887637217085603, 559022711703937487
Offset: 0

Views

Author

Omar E. Pol, Nov 21 2007

Keywords

Comments

Constants (7,5,3,2) are the prime numbers in decreasing order.

Examples

			a(4) = 3123 = 7^4 + 5^4 + 3^4 + 2^4 = 2401 + 625 + 81 + 16.

Links

Crossrefs

Cf. A000079, A000244, A000351, A000420, A001047, A074527, A007689, A135158, A135159, A135160, A001551.

Programs

Formula

From G. C. Greubel, Sep 30 2016: (Start)
a(n) = 17*a(n-1) - 101*a(n-2) + 247*a(n-3) - 210*a(n-4).
G.f.: (4 - 51*x + 202*x^2 - 247*x^3)/((1 -2*x)*(1 -3*x)*(1 -5*x)*(1 -7*x)).
E.g.f.: exp(7*x) + exp(5*x) + exp(3*x) + exp(2*x). (End)

Extensions

Edited by N. J. A. Sloane, Dec 14 2007

A135161 a(n) = 7^n - 5^n - 3^n - 2^n. Constants are the prime numbers in decreasing order.

Original entry on oeis.org

-2, -3, 11, 183, 1679, 13407, 101231, 743103, 5367359, 38380287, 272649551, 1928319423, 13596611039, 95666704767, 672114757871, 4717029550143, 33080299566719, 231867445262847, 1624598512962191, 11379820536259263, 79696895378138399, 558069016462630527, 3907436831406718511
Offset: 0

Views

Author

Omar E. Pol, Nov 21 2007

Keywords

Examples

			a(4) = 1679 because 7^4 = 2401, 5^4 = 625, 3^4 = 81, 2^4 = 16 and we can write 2401 -625 -81 -16 = 1679.

Links

Crossrefs

Cf. A000079, A000244, A000351, A000420, A001047, A074527, A007689, A135158, A135159, A135160.

Programs

  • Magma
    [7^n-5^n-3^n-2^n: n in [0..50]] // Vincenzo Librandi, Dec 14 2010
  • Mathematica
    Table[7^n-5^n-3^n-2^n,{n,0,30}] (* or *) LinearRecurrence[{17,-101,247,-210},{-2,-3,11,183},30] (* Harvey P. Dale, Sep 23 2016 *)
  • PARI
    a(n) = 7^n - 5^n - 3^n - 2^n \\ Charles R Greathouse IV, Sep 30 2016

Formula

From G. C. Greubel, Sep 30 2016: (Start)
a(n) = 17*a(n-1) - 101*a(n-2) + 247*a(n-3) - 210*a(n-4).
G.f.: -x*(-2 + 31 x - 140 x^2 + 187 x^3)/((1 -2*x)*(1 -3*x)*(1 -5*x)*(1 -7*x)).
E.g.f.: exp(7*x) - exp(5*x) - exp(3*x) - exp(2*x). (End)

Extensions

More terms from Vincenzo Librandi, Dec 14 2010

A135162 a(n) = 7^n - 5^n - 3^n + 2^n. Constants are the prime numbers in decreasing order.

Original entry on oeis.org

0, 1, 19, 199, 1711, 13471, 101359, 743359, 5367871, 38381311, 272651599, 1928323519, 13596619231, 95666721151, 672114790639, 4717029615679, 33080299697791, 231867445524991, 1624598513486479, 11379820537307839, 79696895380235551, 558069016466824831, 3907436831415107119
Offset: 0

Views

Author

Omar E. Pol, Nov 21 2007

Keywords

Examples

			a(4) = 1711 because 7^4 = 2401, 5^4 = 625, 3^4 = 81, 2^4 = 16 and 2401-625-81+16 = 1711.

Links

Crossrefs

Cf. A000079, A000244, A000351, A000420, A001047, A074527, A007689, A135158, A135159, A135160.

Programs

  • Magma
    [7^n-5^n-3^n+2^n: n in [0..50]]; // Vincenzo Librandi, Dec 14 2010
  • Mathematica
    Table[7^n-5^n-3^n+2^n,{n,0,30}] (* or *) LinearRecurrence[ {17,-101,247,-210},{0,1,19,199},30] (* Harvey P. Dale, Dec 13 2013 *)
CoefficientList[Series[1/(1 - 7 x) - 1/(1 - 5 x) - 1/(1 - 3 x) + 1/(1 - 2 x), {x, 0, 40}], x] (* Vincenzo Librandi, May 22 2014 *)
  • PARI
    a(n) = 7^n - 5^n - 3^n + 2^n \\ Charles R Greathouse IV, Sep 30 2016

Formula

a(n) = 7^n - 5^n - 3^n + 2^n.
a(0)=0, a(1)=1, a(2)=19, a(3)=199, a(n) = 17*a(n-1) - 101*a(n-2) + 247*a(n-3) - 210*a(n-4). - Harvey P. Dale, Dec 13 2013
G.f.: 1/(1-7*x) - 1/(1-5*x) - 1/(1-3*x) + 1/(1-2 x). - Vincenzo Librandi, May 22 2014
E.g.f.: exp(7*x) - exp(5*x) - exp(3*x) + exp(2*x). - G. C. Greubel, Sep 30 2016

Extensions

More terms from Vincenzo Librandi, Dec 14 2010

A135163 a(n) = 7^n - 5^n + 3^n - 2^n.

Original entry on oeis.org

0, 3, 29, 237, 1841, 13893, 102689, 747477, 5380481, 38419653, 272767649, 1928673717, 13597673921, 95669893413, 672124323809, 4717058247957, 33080385660161, 231867703543173, 1624599287803169, 11379822860782197, 79696902351707201, 558069037383336933, 3907436894168837729
Offset: 0

Views

Author

Omar E. Pol, Nov 21 2007

Keywords

Comments

Constants are the prime numbers in decreasing order.

Examples

			a(4) = 1841 because 7^4 = 2401, 5^4 = 625, 3^4 = 81, 2^4 = 16 and 2401-625+81-16 = 1841.

Links

Crossrefs

Cf. A000079, A000244, A000351, A000420, A001047, A074527, A007689, A135158, A135159, A135160.

Programs

  • Magma
    [7^n-5^n+3^n-2^n: n in [0..50]]; // Vincenzo Librandi, Dec 14 2010
  • Magma
    I:=[0, 3, 29, 237]; [n le 4 select I[n] else 17*Self(n-1)-101*Self(n-2)+247*Self(n-3)-210*Self(n-4): n in [1..30]]; // Vincenzo Librandi, May 22 2014
  • Mathematica
    CoefficientList[Series[1/(1 - 7 x) - 1/(1 - 5 x) + 1/(1 - 3 x) - 1/(1 - 2 x), {x, 0, 40}], x] (* Vincenzo Librandi, May 22 2014 *)
LinearRecurrence[{17,-101,247,-210},{0,3,29,237},30] (* Harvey P. Dale, Sep 17 2016 *)
  • PARI
    a(n) = 7^n - 5^n + 3^n - 2^n \\ Charles R Greathouse IV, Sep 30 2016

Formula

a(n) = 7^n - 5^n + 3^n - 2^n.
from Vincenzo Librandi, May 22 2014: (Start)
G.f.: 1/(1-7*x) - 1/(1-5*x) + 1/(1-3*x) - 1/(1-2*x).
a(n) = 17*a(n-1) - 101*a(n-2) + 247*a(n-3) - 210*a(n-4) for n>3. (End)
E.g.f.: exp(7*x) - exp(5*x) + exp(3*x) - exp(2*x). - G. C. Greubel, Sep 30 2016

Extensions

More terms from Vincenzo Librandi, Dec 14 2010

A135164 a(n) = 7^n - 5^n + 3^n + 2^n.

Original entry on oeis.org

2, 7, 37, 253, 1873, 13957, 102817, 747733, 5380993, 38420677, 272769697, 1928677813, 13597682113, 95669909797, 672124356577, 4717058313493, 33080385791233, 231867703805317, 1624599288327457, 11379822861830773, 79696902353804353, 558069037387531237, 3907436894177226337
Offset: 0

Views

Author

Omar E. Pol, Nov 21 2007

Keywords

Comments

Constants are the prime numbers in decreasing order.

Examples

			a(4) = 1873 because 7^4 = 2401, 5^4 = 625, 3^4 = 81, 2^4 = 16 and 2401-625+81+16 = 1873.

Links

Crossrefs

Cf. A000079, A000244, A000351, A000420, A001047, A074527, A007689, A135158, A135159, A135160.

Programs

  • Magma
    [7^n-5^n+3^n+2^n: n in [0..50]]; // Vincenzo Librandi, Dec 14 2010
  • Magma
    I:=[2,7,37,253]; [n le 4 select I[n] else 17*Self(n-1)-101*Self(n-2)+247*Self(n-3)-210*Self(n-4): n in [1..30]]; // Vincenzo Librandi, May 22 2014
  • Mathematica
    CoefficientList[Series[1/(1 - 7 x) - 1/(1 - 5 x) + 1/(1 - 3 x) + 1/(1 - 2 x), {x, 0, 40}], x] (* Vincenzo Librandi, May 22 2014 *)
Table[7^n-5^n+3^n+2^n,{n,0,30}] (* or *) LinearRecurrence[{17,-101,247,-210},{2,7,37,253},30] (* Harvey P. Dale, Jul 23 2016 *)
  • PARI
    a(n)=7^n-5^n+3^n+2^n \\ Charles R Greathouse IV, Sep 30 2016

Formula

a(n) = 7^n - 5^n + 3^n + 2^n.
From Vincenzo Librandi, May 22 2014: (Start)
G.f.: 1/(1-7*x) - 1/(1-5*x) + 1/(1-3*x) + 1/(1-2*x).
a(n) = 17*a(n-1) - 101*a(n-2) + 247*a(n-3) - 210*a(n-4) for n>3. (End)
E.g.f.: exp(7*x) - exp(5*x) + exp(3*x) + exp(2*x). - G. C. Greubel, Sep 30 2016

Extensions

More terms from Vincenzo Librandi, Dec 14 2010

A135165 a(n) = 7^n + 5^n - 3^n - 2^n.

Original entry on oeis.org

0, 7, 61, 433, 2929, 19657, 132481, 899353, 6148609, 42286537, 292180801, 2025975673, 14084892289, 98108111017, 684321789121, 4778064706393, 33385475347969, 233393324169097, 1632227907493441, 11417967508915513, 79887630241419649, 559022690779036777, 3912205202988749761
Offset: 0

Views

Author

Omar E. Pol, Nov 21 2007

Keywords

Comments

Constants are the prime numbers in decreasing order.

Examples

			a(4) = 2929 because 7^4 = 2401, 5^4 = 625, 3^4 = 81, 2^4 = 16 and 2401+625-81-16 = 2929.

Links

Crossrefs

Cf. A000079, A000244, A000351, A000420, A001047, A074527, A007689, A135158, A135159, A135160.

Programs

  • Magma
    [7^n+5^n-3^n-2^n: n in [0..50]]; // Vincenzo Librandi, Dec 14 2010
  • Magma
    I:=[0,7,61,433]; [n le 4 select I[n] else 17*Self(n-1)-101*Self(n-2)+247*Self(n-3)-210*Self(n-4): n in [1..30]]; // Vincenzo Librandi, May 22 2014
  • Mathematica
    CoefficientList[Series[1/(1 - 7 x) + 1/(1 - 5 x) - 1/(1 - 3 x) - 1/(1 - 2 x), {x, 0, 40}], x] (* Vincenzo Librandi, May 22 2014 *)
LinearRecurrence[{17,-101,247,-210},{0,7,61,433},30] (* Harvey P. Dale, Mar 20 2015 *)
  • PARI
    a(n)=7^n+5^n-3^n-2^n \\ Charles R Greathouse IV, Sep 30 2016

Formula

a(n) = 7^n + 5^n - 3^n - 2^n.
From Vincenzo Librandi, May 22 2014: (Start)
G.f.: 1/(1-7*x) + 1/(1-5*x) - 1/(1-3*x) - 1/(1-2*x).
a(n) = 17*a(n-1) - 101*a(n-2) + 247*a(n-3) - 210*a(n-4) for n>3. (End)
E.g.f.: exp(7*x) + exp(5*x) - exp(3*x) - exp(2*x). - G. C. Greubel, Sep 30 2016

A135166 a(n) = 7^n + 5^n - 3^n + 2^n.

Original entry on oeis.org

2, 11, 69, 449, 2961, 19721, 132609, 899609, 6149121, 42287561, 292182849, 2025979769, 14084900481, 98108127401, 684321821889, 4778064771929, 33385475479041, 233393324431241, 1632227908017729, 11417967509964089, 79887630243516801, 559022690783231081, 3912205202997138369
Offset: 0

Views

Author

Omar E. Pol, Nov 21 2007

Keywords

Comments

Constants are the prime numbers in decreasing order.

Examples

			a(4) = 2961 because 7^4 = 2401, 5^4 = 625, 3^4 = 81, 2^4 = 16 and we can write 2401 + 625 - 81 + 16 = 2961.

Links

Crossrefs

Cf. A000079, A000244, A000351, A000420, A001047, A074527, A007689, A135158, A135159, A135160.

Programs

  • Magma
    [7^n+5^n-3^n+2^n: n in [0..50]] // Vincenzo Librandi, Dec 14 2010
  • Mathematica
    Table[7^n+5^n-3^n+2^n,{n,0,30}] (* or *) LinearRecurrence[ {17,-101,247,-210},{2,11,69,449},30] (* Harvey P. Dale, Feb 01 2013 *)
  • PARI
    a(n)=7^n+5^n-3^n+2^n \\ Charles R Greathouse IV, Sep 30 2016

Formula

a(n) = 7^n + 5^n - 3^n + 2^n.
a(0)=2, a(1)=11, a(2)=69, a(3)=449, a(n) = 17*a(n-1) - 101*a(n-2) + 247*a(n-3) - 210*a(n-4). - Harvey P. Dale, Feb 01 2013
From G. C. Greubel, Sep 30 2016: (Start)
G.f.: (2 - 23*x + 84*x^2 - 107*x^3)/((1 -2*x)*(1 -3*x)*(1 -5*x)*(1 -7*x)).
E.g.f.: exp(7*x) + exp(5*x) - exp(3*x) + exp(2*x). (End)

Extensions

More terms from Vincenzo Librandi, Dec 14 2010

A135167 a(n) = 7^n + 5^n + 3^n - 2^n. Constants are the prime numbers in decreasing order.

Original entry on oeis.org

2, 13, 79, 487, 3091, 20143, 133939, 903727, 6161731, 42325903, 292298899, 2026329967, 14085955171, 98111299663, 684331355059, 4778093404207, 33385561441411, 233393582449423, 1632228682334419, 11417969833438447, 79887637214988451, 559022711699743183, 3912205265750868979
Offset: 0

Views

Author

Omar E. Pol, Nov 21 2007

Keywords

Examples

			a(4)=3091 because 7^4=2401, 5^4=625, 3^4=81, 2^4=16 and we can write 2401+625+81-16=3091.

Links

Crossrefs

Cf. A000079, A000244, A000351, A000420, A001047, A074527, A007689, A135158, A135159, A135160.

Programs

  • Magma
    [7^n+5^n+3^n-2^n: n in [0..50]]; // Vincenzo Librandi, Dec 15 2010
  • Mathematica
    Table[7^n + 5^n + 3^n - 2^n, {n, 0,50}] (* or *) LinearRecurrence[{17, -101, 247, -210}, {2, 13, 79, 487}, 50] (* G. C. Greubel, Sep 30 2016 *)
  • PARI
    a(n)=7^n+5^n+3^n-2^n \\ Charles R Greathouse IV, Sep 30 2016

Formula

a(n) = 7^n + 5^n + 3^n - 2^n.
From G. C. Greubel, Sep 30 2016: (Start)
a(n) = 17*a(n-1) - 101*a(n-2) + 247*a(n-3) - 210*a(n-4).
G.f.: (2 - 21*x + 60*x^2 - 37*x^3)/((1 -2*x)*(1 -3*x)*(1 -5*x)*(1 -7*x)).
E.g.f.: exp(7*x) + exp(5*x) + exp(3*x) - exp(2*x). (End)

Extensions

More terms from Vincenzo Librandi, Dec 15 2010
Showing 1-8 of 8 results.

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

Content is available under The OEIS End-User License Agreement.