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.

A016949 a(n) = (6*n + 3)^5.

Original entry on oeis.org

243, 59049, 759375, 4084101, 14348907, 39135393, 90224199, 184528125, 345025251, 601692057, 992436543, 1564031349, 2373046875, 3486784401, 4984209207, 6956883693, 9509900499, 12762815625, 16850581551, 21924480357, 28153056843, 35723051649, 44840334375, 55730836701
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016757, A016945, A016946, A016947, A016948.
Subsequence of A000584.

Programs

  • Magma
    [(6*n+3)^5: n in [0..50]]; // Vincenzo Librandi, May 05 2011
  • Mathematica
    a[n_] := (6*n + 3)^5; Array[a, 50, 0] (* Amiram Eldar, Mar 30 2022 *)

Formula

From Amiram Eldar, Mar 30 2022: (Start)
a(n) = A016945(n)^5.
a(n) = 3^5*A016757(n).
Sum_{n>=0} 1/a(n) = 31*zeta(5)/7776.
Sum_{n>=0} (-1)^n/a(n) = 5*Pi^5/373248. (End)

A016950 a(n) = (6*n + 3)^6.

Original entry on oeis.org

729, 531441, 11390625, 85766121, 387420489, 1291467969, 3518743761, 8303765625, 17596287801, 34296447249, 62523502209, 107918163081, 177978515625, 282429536481, 433626201009, 646990183449, 941480149401, 1340095640625, 1870414552161, 2565164201769, 3462825991689
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016758, A016945, A016946, A016947, A016948, A016949.
Subsequence of A001014.

Programs

Formula

From Amiram Eldar, Mar 30 2022: (Start)
a(n) = A016945(n)^6 = A016946(n)^3 = A016947(n)^2.
a(n) = 3^6*A016758(n).
Sum_{n>=0} 1/a(n) = Pi^6/699840. (End)

A016951 a(n) = (6*n + 3)^7.

Original entry on oeis.org

2187, 4782969, 170859375, 1801088541, 10460353203, 42618442977, 137231006679, 373669453125, 897410677851, 1954897493193, 3938980639167, 7446353252589, 13348388671875, 22876792454961, 37725479487783, 60170087060757, 93206534790699, 140710042265625, 207616015289871
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016759, A016945, A016946, A016947, A016948, A016949, A016950.
Subsequence of A001015.

Programs

  • Magma
    [(6*n+3)^7: n in [0..40]]; // Vincenzo Librandi, May 05 2011
  • Mathematica
    a[n_] := (6*n + 3)^7; Array[a, 50, 0] (* Amiram Eldar, Mar 30 2022 *)

Formula

From Amiram Eldar, Mar 30 2022: (Start)
a(n) = A016945(n)^7.
a(n) = 3^7*A016759(n).
Sum_{n>=0} 1/a(n) = 127*zeta(7)/279936.
Sum_{n>=0} (-1)^n/a(n) = 61*Pi^7/403107840. (End)

A016952 a(n) = (6*n + 3)^8.

Original entry on oeis.org

6561, 43046721, 2562890625, 37822859361, 282429536481, 1406408618241, 5352009260481, 16815125390625, 45767944570401, 111429157112001, 248155780267521, 513798374428641, 1001129150390625, 1853020188851841, 3282116715437121, 5595818096650401, 9227446944279201
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016760, A016945, A016946, A016947, A016948, A016949, A016950, A016951.
Subsequence of A001016.

Programs

  • Magma
    [(6*n+3)^8: n in [0..40]]; // Vincenzo Librandi, May 05 2011
  • Mathematica
    a[n_] := (6*n + 3)^8; Array[a, 50, 0] (* Amiram Eldar, Mar 30 2022 *)

Formula

From Amiram Eldar, Mar 30 2022: (Start)
a(n) = A016945(n)^8 = A016946(n)^4 = A016948(n)^2.
a(n) = 3^8*A016760(n).
Sum_{n>=0} 1/a(n) = 17*Pi^8/1058158080. (End)

A016953 a(n) = (6*n + 3)^9.

Original entry on oeis.org

19683, 387420489, 38443359375, 794280046581, 7625597484987, 46411484401953, 208728361158759, 756680642578125, 2334165173090451, 6351461955384057, 15633814156853823, 35452087835576229, 75084686279296875, 150094635296999121, 285544154243029527, 520411082988487293
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016761, A016945, A016946, A016947, A016948, A016949, A016950, A016951, A016952.
Subsequence of A001017.

Programs

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, Jan 19 2012
From Amiram Eldar, Mar 30 2022: (Start)
a(n) = A016945(n)^9 = A016947(n)^3.
a(n) = 3^9*A016761(n).
Sum_{n>=0} 1/a(n) = 511*zeta(9)/10077696.
Sum_{n>=0} (-1)^n/a(n) = 277*Pi^9/162533081088. (End)

A016954 a(n) = (6n+3)^10.

Original entry on oeis.org

59049, 3486784401, 576650390625, 16679880978201, 205891132094649, 1531578985264449, 8140406085191601, 34050628916015625, 119042423827613001, 362033331456891249, 984930291881790849, 2446194060654759801, 5631351470947265625, 12157665459056928801
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A008454, A016762, A016945, A016946, A016947, A016948, A016949, A016950, A016951, A016952, A016953.
Subsequence of A008454.

Programs

Formula

From Wesley Ivan Hurt, Aug 22 2016: (Start)
G.f.: 59049*(1 + 59038*x + 9116141*x^2 + 178300904*x^3 + 906923282*x^4 + 1527092468*x^5 + 906923282*x^6 + 178300904*x^7 + 9116141*x^8 + 59038*x^9 + x^10)/(1-x)^11.
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) for n>10.
a(n) = A008454(A016945(n)). (End)
From Amiram Eldar, Mar 30 2022: (Start)
a(n) = A016946(n)^5 = A016949(n)^2.
a(n) = 3^10*A016762(n).
Sum_{n>=0} 1/a(n) = 31*Pi^10/171421608960. (End)

A016955 a(n) = (6*n + 3)^11.

Original entry on oeis.org

177147, 31381059609, 8649755859375, 350277500542221, 5559060566555523, 50542106513726817, 317475837322472439, 1532278301220703125, 6071163615208263051, 20635899893042801193, 62050608388552823487, 168787390185178426269, 422351360321044921875, 984770902183611232881
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016763, A016945, A016946, A016947, A016948, A016949, A016950, A016951, A016952, A016953, A016954.
Subsequence of A008455.

Programs

  • Magma
    [(6*n+3)^11: n in [0..20]]; // Vincenzo Librandi, May 06 2011
  • Mathematica
    a[n_] := (6*n + 3)^11; Array[a, 50, 0] (* Amiram Eldar, Mar 30 2022 *)

Formula

From Amiram Eldar, Mar 30 2022: (Start)
a(n) = A016945(n)^11.
a(n) = 3^11*A016763(n).
Sum_{n>=0} 1/a(n) = 2047*zeta(11)/362797056.
Sum_{n>=0} (-1)^n/a(n) = 50521*Pi^11/2633035913625600. (End)

A016956 a(n) = (6*n + 3)^12.

Original entry on oeis.org

531441, 282429536481, 129746337890625, 7355827511386641, 150094635296999121, 1667889514952984961, 12381557655576425121, 68952523554931640625, 309629344375621415601, 1176246293903439668001, 3909188328478827879681, 11646329922777311412561, 31676352024078369140625
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016764, A016945, A016946, A016947, A016948, A016949, A016950, A016951, A016952, A016953, A016954, A016955.
Subsequence of A008456.

Programs

Formula

From Amiram Eldar, Mar 31 2022: (Start)
a(n) = A016945(n)^12 = A016946(n)^6 = A016947(n)^4 = A016948(n)^3 = A016950(n)^2..
a(n) = 3^12*A016764(n).
Sum_{n>=0} 1/a(n) = 691*Pi^12/339414785740800. (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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