A016783 -id:A016783 - cp's OEIS frontend

A016785 a(n) = (3*n + 1)^9.

1, 262144, 40353607, 1000000000, 10604499373, 68719476736, 322687697779, 1207269217792, 3814697265625, 10578455953408, 26439622160671, 60716992766464, 129961739795077, 262144000000000, 502592611936843, 922190162669056, 1628413597910449, 2779905883635712

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Cf. A016777, A016778, A016779, A016780, A016781, A016782, A016783, A016784.

[(3*n+1)^9 : n in [0..20]]; // Vincenzo Librandi, Sep 28 2011

A016785:=n->(3*n+1)^9; seq(A016785(k), k=0..100); # Wesley Ivan Hurt, Nov 05 2013

Table[(3*n+1)^9, {n,0,100}] (* Wesley Ivan Hurt, Nov 05 2013 *)
LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{1,262144,40353607,1000000000,10604499373,68719476736,322687697779,1207269217792,3814697265625,10578455953408},100] (* Harvey P. Dale, Aug 17 2014 *)

From Amiram Eldar, Mar 29 2022: (Start)
a(n) = A016777(n)^9 = A016779(n)^3.
Sum_{n>=0} 1/a(n) = 1618*Pi^9/(55801305*sqrt(3)) + 9841*zeta(9)/3^9. (End)

A016784 a(n) = (3*n+1)^8.

Original entry on oeis.org

1, 65536, 5764801, 100000000, 815730721, 4294967296, 16983563041, 54875873536, 152587890625, 377801998336, 852891037441, 1785793904896, 3512479453921, 6553600000000, 11688200277601, 20047612231936, 33232930569601, 53459728531456, 83733937890625

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Cf. A001016, A016777, A016778, A016779, A016780, A016781, A016782, A016783.

[(3*n+1)^8 : n in [0..20]]; // Vincenzo Librandi, Sep 28 2011

Table[(3n+1)^8,{n,0,100}] (* Mohammad K. Azarian, Jun 15 2016 *)

A016784(n):=(3*n+1)^8$
makelist(A016784(n),n,0,20); /* Martin Ettl, Nov 12 2012 */

a(n)= A001016(A016777(n)). - Michel Marcus, Jun 15 2016
G.f.: (1 + 65527*x + 5175013*x^2 + 50476003*x^3 + 117758659*x^4 + 77404933*x^5 + 13270807*x^6 + 388321*x^7 + 256*x^8)/(1 - x)^9. - Ilya Gutkovskiy, Jun 16 2016
Sum_{n>=0} 1/a(n) = PolyGamma(7, 1/3)/33067440. - Amiram Eldar, Mar 29 2022

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

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

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

[(6*n+2)^7: n in [0..30]]; // Vincenzo Librandi, May 04 2011

Table[(6n+2)^7,{n,0,100}] (* Mohammad K. Azarian, Jun 15 2016 *)

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)

A016787 a(n) = (3*n + 1)^11.

Original entry on oeis.org

1, 4194304, 1977326743, 100000000000, 1792160394037, 17592186044416, 116490258898219, 584318301411328, 2384185791015625, 8293509467471872, 25408476896404831, 70188843638032384, 177917621779460413, 419430400000000000, 929293739471222707, 1951354384207722496

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Cf. A016777, A016778, A016779, A016780, A016781, A016782, A016783, A016784, A016785, A016786.

Subsequence of A008455.

[(3*n+1)^11: n in [0..20]]; // Vincenzo Librandi, Sep 29 2011

Table[(3*n + 1)^11, {n, 0, 30}] (* Amiram Eldar, Mar 30 2022 *)

From Amiram Eldar, Mar 30 2022: (Start)
a(n) = A016777(n)^11.
Sum_{n>=0} 1/a(n) = 7388*Pi^11/(2511058725*sqrt(3)) + 88573*zeta(11)/177147. (End)
a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12). - Wesley Ivan Hurt, Apr 12 2023

A016786 a(n) = (3*n+1)^10.

Original entry on oeis.org

1, 1048576, 282475249, 10000000000, 137858491849, 1099511627776, 6131066257801, 26559922791424, 95367431640625, 296196766695424, 819628286980801, 2064377754059776, 4808584372417849, 10485760000000000, 21611482313284249, 42420747482776576, 79792266297612001

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Cf. A008454, A016777, A016778, A016779, A016780, A016781, A016782, A016783, A016784, A016785.

[(3*n+1)^10: n in [0..20]]; // Vincenzo Librandi, Sep 29 2011

Table[(3n+1)^10,{n,0,100}] (* Mohammad K. Azarian, Jun 15 2016 *)
LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{1,1048576,282475249,10000000000,137858491849,1099511627776,6131066257801,26559922791424,95367431640625,296196766695424,819628286980801},20] (* Harvey P. Dale, May 14 2019 *)

a(n) = A008454(A016777(n)). - Michel Marcus, Jun 15 2016

Sum_{n>=0} 1/a(n) = PolyGamma(9, 1/3)/21427701120. - Amiram Eldar, Mar 29 2022

A016788 a(n) = (3*n+1)^12.

Original entry on oeis.org

1, 16777216, 13841287201, 1000000000000, 23298085122481, 281474976710656, 2213314919066161, 12855002631049216, 59604644775390625, 232218265089212416, 787662783788549761, 2386420683693101056, 6582952005840035281, 16777216000000000000, 39959630797262576401

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Cf. A008456, A016777, A016778, A016779, A016780, A016781, A016782, A016783, A016784, A016785, A016786, A016787.

Subsequence of A008456.

[(3*n+1)^12: n in [0..20]]; // Vincenzo Librandi, Sep 29 2011

Table[(3n+1)^12,{n,0,100}] (* Mohammad K. Azarian, Jun 15 2016 *)

a(n) = A008456(A016777(n)). - Michel Marcus, Jun 16 2016

Sum_{n>=0} 1/a(n) = PolyGamma(11, 1/3)/21213424108800. - Amiram Eldar, Mar 30 2022

A017203 a(n) = (9*n + 3)^7.

Original entry on oeis.org

2187, 35831808, 1801088541, 21870000000, 137231006679, 587068342272, 1954897493193, 5455160701056, 13348388671875, 29509034655744, 60170087060757, 114868566764928, 207616015289871, 358318080000000, 594467302491009, 953133216331392, 1483273860320763, 2248392813428736

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Cf. A013665, A016783, A017197.

[(9*n+3)^7: n in [0..20]]; // Vincenzo Librandi, Jul 23 2011

Table[(9*n + 3)^7, {n, 0, 20}] (* Amiram Eldar, Oct 03 2024 *)

From Amiram Eldar, Oct 03 2024: (Start)
a(n) = A017197(n)^7 = 3^7 * A016783(n).
Sum_{n>=0} 1/a(n) = 28*Pi^7/(215233605*sqrt(3)) + 1093*zeta(7)/4782969. (End)

A017575 a(n) = (12n+4)^7.

Original entry on oeis.org

16384, 268435456, 13492928512, 163840000000, 1028071702528, 4398046511104, 14645194571776, 40867559636992, 100000000000000, 221068140740608, 450766669594624, 860542568759296, 1555363874947072, 2684354560000000, 4453476124377088, 7140436495826944, 11112006825558016

Offset: 0

N. J. A. Sloane

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Cf. A001015, A013665, A016783, A017569.

a[n_] := (12*n + 4)^7; Array[a, 20, 0] (* Amiram Eldar, Jul 14 2024 *)

From Amiram Eldar, Jul 14 2024: (Start)
a(n) = A001015(A017569(n)) = A017569(n)^7.
a(n) = 16384 * A016783(n).
Sum_{n>=0} 1/a(n) = 7*Pi^7/(403107840*sqrt(3)) + 1093*zeta(7)/35831808. (End)

More terms from Amiram Eldar, Jul 14 2024

cp's OEIS Frontend

A016785 a(n) = (3*n + 1)^9.

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A016784 a(n) = (3*n+1)^8.

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

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Magma

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A016787 a(n) = (3*n + 1)^11.

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Magma

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A016786 a(n) = (3*n+1)^10.

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Magma

Mathematica

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A016788 a(n) = (3*n+1)^12.

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Magma

Mathematica

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A017203 a(n) = (9*n + 3)^7.

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Magma

Mathematica

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A017575 a(n) = (12n+4)^7.

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