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 1-9 of 9 results.

A016936 a(n) = (6*n + 2)^4.

Original entry on oeis.org

16, 4096, 38416, 160000, 456976, 1048576, 2085136, 3748096, 6250000, 9834496, 14776336, 21381376, 29986576, 40960000, 54700816, 71639296, 92236816, 116985856, 146410000, 181063936, 221533456, 268435456, 322417936, 384160000, 454371856, 533794816, 623201296
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016780, A016933, A016934, A016935.

Programs

  • Magma
    [(6*n+2)^4: n in [0..30]]; // Vincenzo Librandi, May 04 2011
  • Mathematica
    (6*Range[0,30]+2)^4 (* or *) LinearRecurrence[{5,-10,10,-5,1},{16,4096,38416,160000,456976},30] (* Harvey P. Dale, Aug 22 2012 *)

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, Aug 22 2012
From Amiram Eldar, Mar 29 2022: (Start)
a(n) = A016933(n)^4 = A016934(n)^2.
a(n) = 16*A016780(n).
Sum_{n>=0} 1/a(n) = PolyGamma(3, 1/3)/7776. (End)

A016937 a(n) = (6*n + 2)^5.

Original entry on oeis.org

32, 32768, 537824, 3200000, 11881376, 33554432, 79235168, 164916224, 312500000, 550731776, 916132832, 1453933568, 2219006624, 3276800000, 4704270176, 6590815232, 9039207968, 12166529024, 16105100000, 21003416576, 27027081632, 34359738368, 43204003424, 53782400000
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016781, A016933, A016934, A016935, A016936.

Programs

  • Magma
    [(6*n+2)^5: n in [0..30]]; // Vincenzo Librandi, May 04 2011
  • Mathematica
    (6*Range[0,20]+2)^5 (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{32,32768,537824,3200000,11881376,33554432},20] (* Harvey P. Dale, Dec 13 2012 *)

Formula

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). - Harvey P. Dale, Dec 13 2012
From Amiram Eldar, Mar 29 2022: (Start)
a(n) = A016933(n)^5.
a(n) = 32*A016781(n).
Sum_{n>=0} 1/a(n) = Pi^5/(11664*sqrt(3)) + 121*zeta(5)/7776. (End)

A016938 a(n) = (6*n + 2)^6.

Original entry on oeis.org

64, 262144, 7529536, 64000000, 308915776, 1073741824, 3010936384, 7256313856, 15625000000, 30840979456, 56800235584, 98867482624, 164206490176, 262144000000, 404567235136, 606355001344, 885842380864, 1265319018496, 1771561000000, 2436396322816, 3297303959104
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016782, A016933, A016934, A016935, A016936, A016937.

Programs

Formula

From Amiram Eldar, Mar 29 2022: (Start)
a(n) = A016933(n)^6 = A016934(n)^3 = A016935(n)^2.
a(n) = 64*A016782(n).
Sum_{n>=0} 1/a(n) = PolyGamma(5, 1/3)/5598720. (End)

A016939 a(n) = (6n+2)^7.

Original entry on oeis.org

128, 2097152, 105413504, 1280000000, 8031810176, 34359738368, 114415582592, 319277809664, 781250000000, 1727094849536, 3521614606208, 6722988818432, 12151280273024, 20971520000000, 34792782221696, 55784660123648, 86812553324672, 131593177923584, 194871710000000
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016783, A016933, A016934, A016935, A016936, A016937, A016938.

Programs

Formula

a(n) = 128*A016783(n). - R. J. Mathar, May 07 2008
G.f.: 128*(1 + 16376*x + 692499*x^2 + 3870352*x^3 + 4890287*x^4 + 1475736*x^5 + 77101*x^6 + 128*x^7)/(1 - x)^8. - Ilya Gutkovskiy, Jun 16 2016
From Amiram Eldar, Mar 29 2022: (Start)
a(n) = A016933(n)^7.
Sum_{n>=0} 1/a(n) = 7*Pi^7/(3149280*sqrt(3)) + 1093*zeta(7)/279936. (End)

A016940 a(n) = (6*n + 2)^8.

Original entry on oeis.org

256, 16777216, 1475789056, 25600000000, 208827064576, 1099511627776, 4347792138496, 14048223625216, 39062500000000, 96717311574016, 218340105584896, 457163239653376, 899194740203776, 1677721600000000, 2992179271065856, 5132188731375616, 8507630225817856
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016784, A016933, A016934, A016935, A016936, A016937, A016938, A016939.

Programs

  • Magma
    [(6*n+2)^8: n in [0..20]]; // Vincenzo Librandi, May 04 2011
  • Mathematica
    (6*Range[0,20]+2)^8 (* or *) LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{256,16777216,1475789056,25600000000,208827064576,1099511627776,4347792138496,14048223625216,39062500000000},20] (* Harvey P. Dale, Sep 06 2020 *)

Formula

From Amiram Eldar, Mar 29 2022: (Start)
a(n) = A016933(n)^8 = A016934(n)^4 = A016936(n)^2.
a(n) = 2^8*A016784(n).
Sum_{n>=0} 1/a(n) = PolyGamma(7, 1/3)/8465264640. (End)

A016941 a(n) = (6*n + 2)^9.

Original entry on oeis.org

512, 134217728, 20661046784, 512000000000, 5429503678976, 35184372088832, 165216101262848, 618121839509504, 1953125000000000, 5416169448144896, 13537086546263552, 31087100296429568, 66540410775079424, 134217728000000000, 257327417311663616, 472161363286556672
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016785, A016933, A016934, A016935, A016936, A016937, A016938, A016939, A016940.

Programs

  • Magma
    [(6*n+2)^9: n in [0..25]]; // Vincenzo Librandi, May 05 2011
  • Mathematica
    (6*Range[0,20]+2)^9 (* or *) LinearRecurrence[ {10,-45,120,-210,252,-210,120,-45,10,-1},{512,134217728,20661046784,512000000000,5429503678976,35184372088832,165216101262848,618121839509504,1953125000000000,5416169448144896},20] (* Harvey P. Dale, Sep 21 2013 *)

Formula

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10). - Harvey P. Dale, Sep 21 2013
From Amiram Eldar, Mar 29 2022: (Start)
a(n) = A016933(n)^9 = A016935(n)^3.
a(n) = 2^9*A016785(n).
Sum_{n>=0} 1/a(n) = 809*Pi^9/(14285134080*sqrt(3)) + 9841*zeta(9)/10077696. (End)

A016942 a(n) = (6*n + 2)^10.

Original entry on oeis.org

1024, 1073741824, 289254654976, 10240000000000, 141167095653376, 1125899906842624, 6278211847988224, 27197360938418176, 97656250000000000, 303305489096114176, 839299365868340224, 2113922820157210624, 4923990397355877376, 10737418240000000000, 22130157888803070976
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016786, A016933, A016934, A016935, A016936, A016937, A016938, A016939, A016940, A016941.

Programs

Formula

From Amiram Eldar, Mar 29 2022: (Start)
a(n) = A016933(n)^10 = A016934(n)^5 = A016937(n)^2.
a(n) = 2^10*A016786(n).
Sum_{n>=0} 1/a(n) = PolyGamma(9, 1/3)/21941965946880. (End)

A016943 a(n) = (6*n + 2)^11.

Original entry on oeis.org

2048, 8589934592, 4049565169664, 204800000000000, 3670344486987776, 36028797018963968, 238572050223552512, 1196683881290399744, 4882812500000000000, 16985107389382393856, 52036560683837093888, 143746751770690322432, 364375289404334925824, 858993459200000000000
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016787, A016933, A016934, A016935, A016936, A016937, A016938, A016939, A016940, A016941, A016942.
Subsequence of A008455.

Programs

Formula

a(n) = A016787(n)*2^11. - Zerinvary Lajos, Jun 22 2009
From Amiram Eldar, Mar 30 2022: (Start)
a(n) = A016933(n)^9 = A016935(n)^3.
Sum_{n>=0} 1/a(n) = 1847*Pi^11/(1285662067200*sqrt(3)) + 88573*zeta(11)/362797056. (End)

A016944 a(n) = (6*n + 2)^12.

Original entry on oeis.org

4096, 68719476736, 56693912375296, 4096000000000000, 95428956661682176, 1152921504606846976, 9065737908494995456, 52654090776777588736, 244140625000000000000, 951166013805414055936, 3226266762397899821056, 9774779120406941925376, 26963771415920784510976
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016788, A016933, A016934, A016935, A016936, A016937, A016938, A016939, A016940, A016941, A016942, A016943.
Subsequence of A008456.

Programs

  • Magma
    [(6*n+2)^12: n in [0..20]]; // Vincenzo Librandi, May 05 2011
  • Mathematica
    (6*Range[0,20]+2)^12 (* or *) LinearRecurrence[{13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1},{4096,68719476736,56693912375296,4096000000000000,95428956661682176,1152921504606846976,9065737908494995456,52654090776777588736,244140625000000000000,951166013805414055936,3226266762397899821056,9774779120406941925376,26963771415920784510976},20] (* Harvey P. Dale, Aug 03 2021 *)

Formula

From Amiram Eldar, Mar 30 2022: (Start)
a(n) = A016933(n)^12 = A016934(n)^6 = A016935(n)^4 = A016936(n)^3 = A016938(n)^2.
a(n) = 2^12*A016788(n).
Sum_{n>=0} 1/a(n) = PolyGamma(11, 1/3)/86890185149644800. (End)
Showing 1-9 of 9 results.

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

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