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.

A016960 a(n) = (6*n + 4)^4.

Original entry on oeis.org

256, 10000, 65536, 234256, 614656, 1336336, 2560000, 4477456, 7311616, 11316496, 16777216, 24010000, 33362176, 45212176, 59969536, 78074896, 100000000, 126247696, 157351936, 193877776, 236421376, 285610000, 342102016, 406586896, 479785216, 562448656, 655360000
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016792, A016957, A016958, A016959.
Subsequence of A000583.

Programs

  • Magma
    [(6*n+4)^4: n in [0..40]]; // Vincenzo Librandi, May 06 2011
  • Mathematica
    (6*Range[0,20]+4)^4 (* or *) LinearRecurrence[{5,-10,10,-5,1},{256,10000,65536,234256,614656},30] (* Harvey P. Dale, Sep 23 2013 *)

Formula

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Harvey P. Dale, Sep 23 2013
G.f.: 16*(16+545*x+1131*x^2+251*x^3+x^4)/(1-x)^5. - Harvey P. Dale, Aug 21 2021
From Amiram Eldar, Mar 31 2022: (Start)
a(n) = A016957(n)^4 = A016958(n)^2.
a(n) = 16*A016792(n).
Sum_{n>=0} 1/a(n) = PolyGamma(3, 2/3)/7776. (End)

A016793 a(n) = (3*n + 2)^5.

Original entry on oeis.org

32, 3125, 32768, 161051, 537824, 1419857, 3200000, 6436343, 11881376, 20511149, 33554432, 52521875, 79235168, 115856201, 164916224, 229345007, 312500000, 418195493, 550731776, 714924299, 916132832, 1160290625, 1453933568, 1804229351, 2219006624, 2706784157, 3276800000
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016789, A016790, A016791, A016792.
Subsequence of A000584.

Programs

  • Magma
    [(3*n+2)^5 : n in [0..30]]; // Vincenzo Librandi, Sep 29 2011
  • Mathematica
    Table[(3n+2)^5,{n,0,100}] (* Mohammad K. Azarian, Jun 15 2016 *)
LinearRecurrence[{6,-15,20,-15,6,-1},{32,3125,32768,161051,537824,1419857},30] (* Harvey P. Dale, May 10 2024 *)

Formula

From Ilya Gutkovskiy, Jun 16 2016: (Start)
G.f.: (32 + 2933*x + 14498*x^2 + 10678*x^3 + 1018*x^4 + x^5)/(1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). (End)
From Amiram Eldar, Mar 31 2022: (Start)
a(n) = A016789(n)^5.
Sum_{n>=0} 1/a(n) = 121*zeta(5)/243 - 2*Pi^5/(729*sqrt(3)). (End)

A016794 a(n) = (3*n + 2)^6.

Original entry on oeis.org

64, 15625, 262144, 1771561, 7529536, 24137569, 64000000, 148035889, 308915776, 594823321, 1073741824, 1838265625, 3010936384, 4750104241, 7256313856, 10779215329, 15625000000, 22164361129, 30840979456, 42180533641, 56800235584, 75418890625, 98867482624, 128100283921
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016789, A016790, A016791, A016792, A016793.
Subsequence of A001014.

Programs

Formula

From Amiram Eldar, Mar 31 2022: (Start)
a(n) = A016789(n)^6 = A016790(n)^3 = A016791(n)^2.
Sum_{n>=0} 1/a(n) = PolyGamma(5, 2/3)/87480. (End)

A016796 a(n) = (3*n + 2)^8.

Original entry on oeis.org

256, 390625, 16777216, 214358881, 1475789056, 6975757441, 25600000000, 78310985281, 208827064576, 500246412961, 1099511627776, 2251875390625, 4347792138496, 7984925229121, 14048223625216, 23811286661761, 39062500000000, 62259690411361, 96717311574016, 146830437604321
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016789, A016790, A016791, A016792, A016793, A016794, A016795.
Subsequence of A001016.

Programs

  • Mathematica
    (3 Range[0, 20] + 2)^8 (* Harvey P. Dale, Jan 24 2011 *)

Formula

From Amiram Eldar, Mar 31 2022: (Start)
a(n) = A016789(n)^6 = A016790(n)^3 = A016791(n)^2.
Sum_{n>=0} 1/a(n) = PolyGamma(7, 2/3)/33067440. (End)

A016798 a(n) = (3*n + 2)^10.

Original entry on oeis.org

1024, 9765625, 1073741824, 25937424601, 289254654976, 2015993900449, 10240000000000, 41426511213649, 141167095653376, 420707233300201, 1125899906842624, 2758547353515625, 6278211847988224, 13422659310152401, 27197360938418176, 52599132235830049
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016789, A016790, A016791, A016792, A016793, A016794, A016795.
Subsequence of A008454.

Programs

Formula

From Harvey P. Dale, Nov 28 2014: (Start)
G.f.: -(1/((x-1)^11))(x^10+1048565*x^9+270940968*x^8+6950443776*x^7+ 43221615834*x^6+86805830970*x^5+61387794480*x^4+14663204952*x^3+ 966376269*x^2+9754361*x+1024).
a(n) = 59049*n^10 + 393660*n^9 + 1180980*n^8 + 2099520*n^7 + 2449440*n^6 + 1959552*n^5 + 1088640*n^4 + 414720*n^3 + 103680*n^2 + 15360*n + 1024. [corrected by Amiram Eldar, Mar 31 2022] (End)
From Amiram Eldar, Mar 31 2022: (Start)
a(n) = A016789(n)^10 = A016790(n)^5 = A016793(n)^2.
Sum_{n>=0} 1/a(n) = PolyGamma(9, 2/3)/21427701120. (End)
a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11). - Wesley Ivan Hurt, Dec 31 2023

A016797 a(n) = (3*n + 2)^9.

Original entry on oeis.org

512, 1953125, 134217728, 2357947691, 20661046784, 118587876497, 512000000000, 1801152661463, 5429503678976, 14507145975869, 35184372088832, 78815638671875, 165216101262848, 327381934393961, 618121839509504, 1119130473102767, 1953125000000000, 3299763591802133
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016789, A016790, A016791, A016792, A016793, A016794, A016795, A016796.
Subsequence of A001017.

Programs

Formula

G.f.: (512 + 1948005*x + 114709518*x^2 + 1103599596*x^3 + 2887100154*x^4 + 2388954618*x^5 + 608260290*x^6 + 37732212*x^7 + 262134*x^8 + x^9)/(1 - x)^10. - Ilya Gutkovskiy, Jun 16 2016
From Amiram Eldar, Mar 31 2022: (Start)
a(n) = A016789(n)^9.
Sum_{n>=0} 1/a(n) = 9841*zeta(9)/19683 - 1618*Pi^9/(55801305*sqrt(3)). (End)

A016799 a(n) = (3*n + 2)^11.

Original entry on oeis.org

2048, 48828125, 8589934592, 285311670611, 4049565169664, 34271896307633, 204800000000000, 952809757913927, 3670344486987776, 12200509765705829, 36028797018963968, 96549157373046875, 238572050223552512, 550329031716248441, 1196683881290399744, 2472159215084012303
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016789, A016790, A016791, A016792, A016793, A016794, A016795, A016796, A016797, A016798.
Subsequence of A008455.

Programs

Formula

From Amiram Eldar, Apr 01 2022: (Start)
a(n) = A016789(n)^11.
Sum_{n>=0} 1/a(n) = 88573*zeta(11)/177147 - 7388*Pi^11/(2511058725*sqrt(3)). (End)

A016800 a(n) = (3*n + 2)^12.

Original entry on oeis.org

4096, 244140625, 68719476736, 3138428376721, 56693912375296, 582622237229761, 4096000000000000, 21914624432020321, 95428956661682176, 353814783205469041, 1152921504606846976, 3379220508056640625, 9065737908494995456, 22563490300366186081, 52654090776777588736
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016789, A016790, A016791, A016792, A016793, A016794, A016795, A016796, A016797, A016798, A016799.
Subsequence of A008456.

Programs

Formula

From Amiram Eldar, Apr 01 2022: (Start)
a(n) = A016789(n)^12 = A016790(n)^6 = A016791(n)^4 = A016792(n)^3 = A016794(n)62.
Sum_{n>=0} 1/a(n) = PolyGamma(11, 2/3)/21213424108800. (End)
Showing 1-8 of 8 results.

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

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