A016779 -id:A016779 - cp's OEIS frontend

A061102 Duplicate of A016779.

1, 64, 343, 1000, 2197, 4096, 6859, 10648, 15625, 21952, 29791, 39304, 50653, 64000, 79507, 97336, 117649, 140608, 166375, 195112, 226981, 262144, 300763, 343000, 389017, 438976, 493039, 551368, 614125, 681472, 753571, 830584, 912673, 1000000

Offset: 0

dead

A016777 a(n) = 3*n + 1.

Original entry on oeis.org

1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 130, 133, 136, 139, 142, 145, 148, 151, 154, 157, 160, 163, 166, 169, 172, 175, 178, 181, 184, 187

Offset: 0

N. J. A. Sloane, Dec 11 1996

Numbers k such that the concatenation of the first k natural numbers is not divisible by 3. E.g., 16 is in the sequence because we have 123456789101111213141516 == 1 (mod 3).
Ignoring the first term, this sequence represents the number of bonds in a hydrocarbon: a(#of carbon atoms) = number of bonds. - Nathan Savir (thoobik(AT)yahoo.com), Jul 03 2003
n such that Sum_{k=0..n} (binomial(n+k,n-k) mod 2) is even (cf. A007306). - Benoit Cloitre, May 09 2004
Hilbert series for twisted cubic curve. - Paul Barry, Aug 11 2006
If Y is a 3-subset of an n-set X then, for n >= 3, a(n-3) is the number of 3-subsets of X having at least two elements in common with Y. - Milan Janjic, Nov 23 2007
a(n) = A144390 (1, 9, 23, 43, 69, ...) - A045944 (0, 5, 16, 33, 56, ...). From successive spectra of hydrogen atom. - Paul Curtz, Oct 05 2008
Number of monomials in the n-th power of polynomial x^3+x^2+x+1. - Artur Jasinski, Oct 06 2008
A145389(a(n)) = 1. - Reinhard Zumkeller, Oct 10 2008
Union of A035504, A165333 and A165336. - Reinhard Zumkeller, Sep 17 2009
Hankel transform of A076025. - Paul Barry, Sep 23 2009
From Jaroslav Krizek, May 28 2010: (Start)
a(n) = numbers k such that the antiharmonic mean of the first k positive integers is an integer.
A169609(a(n-1)) = 1. See A146535 and A169609. Complement of A007494.
See A005408 (odd positive integers) for corresponding values A146535(a(n)). (End)
Apart from the initial term, A180080 is a subsequence; cf. A180076. - Reinhard Zumkeller, Aug 14 2010
Also the maximum number of triangles that n + 2 noncoplanar points can determine in 3D space. - Carmine Suriano, Oct 08 2010
A089911(4*a(n)) = 3. - Reinhard Zumkeller, Jul 05 2013
The number of partitions of 6*n into at most 2 parts. - Colin Barker, Mar 31 2015
For n >= 1, a(n)/2 is the proportion of oxygen for the stoichiometric combustion reaction of hydrocarbon CnH2n+2, e.g., one part propane (C3H8) requires 5 parts oxygen to complete its combustion. - Kival Ngaokrajang, Jul 21 2015
Exponents n > 0 for which 1 + x^2 + x^n is reducible. - Ron Knott, Oct 13 2016
Also the number of independent vertex sets in the n-cocktail party graph. - Eric W. Weisstein, Sep 21 2017
Also the number of (not necessarily maximal) cliques in the n-ladder rung graph. - Eric W. Weisstein, Nov 29 2017
Also the number of maximal and maximum cliques in the n-book graph. - Eric W. Weisstein, Dec 01 2017
For n>=1, a(n) is the size of any snake-polyomino with n cells. - Christian Barrientos and Sarah Minion, Feb 27 2018
The sum of two distinct terms of this sequence is never a square. See Lagarias et al. p. 167. - Michel Marcus, May 20 2018
It seems that, for any n >= 1, there exists no positive integer z such that digit_sum(a(n)*z) = digit_sum(a(n)+z). - Max Lacoma, Sep 18 2019
For n > 2, a(n-2) is the number of distinct values of the magic constant in a normal magic triangle of order n (see formula 5 in Trotter). - Stefano Spezia, Feb 18 2021
Number of 3-permutations of n elements avoiding the patterns 132, 231, 312. See Bonichon and Sun. - Michel Marcus, Aug 20 2022
Erdős & Sárközy conjecture that a set of n positive integers with property P must have some element at least a(n-1) = 3n - 2. Property P states that, for x, y, and z in the set and z < x, y, z does not divide x+y. An example of such a set is {2n-1, 2n, ..., 3n-2}. Bedert proves this for large enough n. (This is an upper bound, and is exact for all known n; I have verified it for n up to 12.) - Charles R Greathouse IV, Feb 06 2023
a(n-1) = 3*n-2 is the dimension of the vector space of all n X n tridiagonal matrices, equals the number of nonzero coefficients: n + 2*(n-1) (see Wikipedia link). - Bernard Schott, Mar 03 2023

			G.f. = 1 + 4*x + 7*x^2 + 10*x^3 + 13*x^4 + 16*x^5 + 19*x^6 + 22*x^7 + ... - _Michael Somos_, May 27 2019

W. Decker, C. Lossen, Computing in Algebraic Geometry, Springer, 2006, p. 22.
Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, §8.1 Terminology, p. 264.
Konrad Knopp, Theory and Application of Infinite Series, Dover, p. 269.

N. J. A. Sloane, Table of n, a(n) for n = 0..10000
Hacène Belbachir, Toufik Djellal, and Jean-Gabriel Luque, On the self-convolution of generalized Fibonacci numbers, arXiv:1703.00323 [math.CO], 2017.
Benjamin Bedert, On a problem of Erdős and Sárközy about sequences with no term dividing the sum of two larger terms, arXiv preprint, arXiv:2301.07065 [math.NT], 2023.
Nicolas Bonichon and Pierre-Jean Morel, Baxter d-permutations and other pattern avoiding classes, arXiv:2202.12677 [math.CO], 2022.
Paul Erdős and András Sárközy, On the divisibility properties of sequences of integers, Proc. London Math. Soc. (3), 21 (1970), pp. 97-101.
Leonhard Euler, Observatio de summis divisorum p. 9.
Leonhard Euler, An observation on the sums of divisors, arXiv:math/0411587 [math.HO], 2004-2009, see p. 9.
L. B. W. Jolley, Summation of Series, Dover, 1961, pp. 16, 38.
Tanya Khovanova, Recursive Sequences
Konrad Knopp, Theorie und Anwendung der unendlichen Reihen, Berlin, J. Springer, 1922. (Original German edition of "Theory and Application of Infinite Series")
J. C. Lagarias, A. M. Odlyzko, and J. B. Shearer, On the density of sequences of integers the sum of no two of which is a square. I. Arithmetic progressions, Journal of Combinatorial Theory. Series A, 33 (1982), pp. 167-185.
T. Mansour, Permutations avoiding a set of patterns from S_3 and a pattern from S_4, arXiv:math/9909019 [math.CO], 1999.
Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014.
Nathan Sun, On d-permutations and Pattern Avoidance Classes, arXiv:2208.08506 [math.CO], 2022.
Terrel Trotter, Normal Magic Triangles of Order n, Journal of Recreational Mathematics Vol. 5, No. 1, 1972, pp. 28-32.
Eric Weisstein's World of Mathematics, Book Graph
Eric Weisstein's World of Mathematics, Clique
Eric Weisstein's World of Mathematics, Cocktail Party Graph
Eric Weisstein's World of Mathematics, Independent Vertex Set
Eric Weisstein's World of Mathematics, Ladder Rung Graph
Eric Weisstein's World of Mathematics, Maximal Clique
Eric Weisstein's World of Mathematics, Maximum Clique
Wikipedia, Tridiagonal matrix.
Chengcheng Yang, A Problem of Erdös Concerning Lattice Cubes, arXiv:2011.15010 [math.CO], 2020. See Table p. 27.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A000290, A001477, A005408, A007306, A007494, A016789, A016933.
Cf. A017569, A035504, A045944, A058183, A076025, A089911, A144390.
Cf. A145389, A146535, A165333, A165336, A169609, A180076, A180080.
Cf. A214550, A238731.
Cf. A007559 (partial products), A051536 (lcm).
First differences of A000326.
Row sums of A131033.
Complement of A007494. - Reinhard Zumkeller, Oct 10 2008
Some subsequences: A002476 (primes), A291745 (nonprimes), A135556 (squares), A016779 (cubes).

a016777 = (+ 1) . (* 3)
a016777_list = [1, 4 ..]  -- Reinhard Zumkeller, Feb 28 2013, Feb 10 2012

[3*n+1 : n in [1..70]]; // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006

Range[1, 199, 3] (* Vladimir Joseph Stephan Orlovsky, May 26 2011 *)
(* Start from Eric W. Weisstein, Sep 21 2017 *)
3 Range[0, 70] + 1
Table[3 n + 1, {n, 0, 70}]
LinearRecurrence[{2, -1}, {1, 4}, 70]
CoefficientList[Series[(1 + 2 x)/(-1 + x)^2, {x, 0, 70}], x]
(* End *)

A016777(n):=3*n+1$
makelist(A016777(n),n,0,30); /* Martin Ettl, Oct 31 2012 */

a(n)=3*n+1 \\ Charles R Greathouse IV, Jul 28 2015

[3*n+1 for n in range(1,71)] # G. C. Greubel, Mar 15 2024

G.f.: (1+2*x)/(1-x)^2.
a(n) = A016789(n) - 1.
a(n) = 3 + a(n-1).
Sum_{n>=1} (-1)^n/a(n) = (1/3)*(Pi/sqrt(3) + log(2)). [Jolley, p. 16, (79)] - Benoit Cloitre, Apr 05 2002
(1 + 4*x + 7*x^2 + 10*x^3 + ...) = (1 + 2*x + 3*x^2 + ...)/(1 - 2*x + 4*x^2 - 8*x^3 + ...). - Gary W. Adamson, Jul 03 2003
E.g.f.: exp(x)*(1+3*x). - Paul Barry, Jul 23 2003
a(n) = 2*a(n-1) - a(n-2); a(0)=1, a(1)=4. - Philippe Deléham, Nov 03 2008
a(n) = 6*n - a(n-1) - 1 (with a(0) = 1). - Vincenzo Librandi, Nov 20 2010
Sum_{n>=0} 1/a(n)^2 = A214550. - R. J. Mathar, Jul 21 2012
a(n) = A238731(n+1,n) = (-1)^n*Sum_{k = 0..n} A238731(n,k)*(-5)^k. - Philippe Deléham, Mar 05 2014
Sum_{i=0..n} (a(i)-i) = A000290(n+1). - Ivan N. Ianakiev, Sep 24 2014
From Wolfdieter Lang, Mar 09 2018: (Start)
a(n) = denominator(Sum_{k=0..n-1} 1/(a(k)*a(k+1))), with the numerator n = A001477(n), where the sum is set to 0 for n = 0. [Jolley, p. 38, (208)]
G.f. for {n/(1 + 3*n)}_{n >= 0} is (1/3)*(1-hypergeom([1, 1], [4/3], -x/(1-x)))/(1-x). (End)
a(n) = -A016789(-1-n) for all n in Z. - Michael Somos, May 27 2019

Better description from T. D. Noe, Aug 15 2002

Partially edited by Joerg Arndt, Mar 11 2010

A016778 a(n) = (3*n+1)^2.

Original entry on oeis.org

1, 16, 49, 100, 169, 256, 361, 484, 625, 784, 961, 1156, 1369, 1600, 1849, 2116, 2401, 2704, 3025, 3364, 3721, 4096, 4489, 4900, 5329, 5776, 6241, 6724, 7225, 7744, 8281, 8836, 9409, 10000, 10609, 11236, 11881, 12544, 13225, 13924, 14641, 15376, 16129, 16900, 17689

Offset: 0

N. J. A. Sloane

From Paul Curtz, Mar 28 2019: (Start)
Sequence is a spoke of the hexagonal spiral built from the terms of A016777:
.
        \
       100--97--94--91
          \           \
          49--46--43  88
          / \       \   \
        52  16--13  40  85
        /   / \   \   \   \
      55  19   1  10  37  82
      /   /   /   /   /   /
    58  22   4---7  34  79
      \   \         /   /
      61  25--28--31  76
        \             /
        64--67--70--73
(End)

Shawn A. Broyles, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A000212, A000290, A016777, A016779, A016780, A016781, A214550, A247792, A262178.

(3*Range[0,50]+1)^2 (* or *) LinearRecurrence[{3,-3,1},{1,16,49},50] (* Harvey P. Dale, Mar 03 2013 *)

A016778(n):=(3*n+1)^2$
makelist(A016778(n),n,0,20); /* Martin Ettl, Nov 12 2012 */

a(n)=(3*n+1)^2 \\ Charles R Greathouse IV, Oct 07 2015

a(n) = a(n-1) + 3*(6*n-1); a(0)=1. - Vincenzo Librandi, Nov 20 2010
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=1, a(1)=16, a(2)=49. - Harvey P. Dale, Mar 03 2013
a(n) = A247792(n) + 6*n. - Miquel Cerda, Oct 23 2016
G.f.: (1 + 13*x + 4*x^2)/(1 - x)^3. - Ilya Gutkovskiy, Oct 23 2016
a(n) = A000212(3*n) + A000212(1+3*n) + A000212(2+3*n). - Paul Curtz, Mar 28 2019
From Amiram Eldar, Nov 12 2020: (Start)
Sum_{n>=0} 1/a(n) = A214550.
Sum_{n>=0} (-1)^n/a(n) = A262178. (End)
From Elmo R. Oliveira, May 29 2025: (Start)
E.g.f.: exp(x)*(1 + 15*x + 9*x^2).
a(n) = A000290(A016777(n)) = A016777(n)^2. (End)

A016791 a(n) = (3*n + 2)^3.

Original entry on oeis.org

8, 125, 512, 1331, 2744, 4913, 8000, 12167, 17576, 24389, 32768, 42875, 54872, 68921, 85184, 103823, 125000, 148877, 175616, 205379, 238328, 274625, 314432, 357911, 405224, 456533, 512000, 571787, 636056, 704969, 778688, 857375, 941192, 1030301, 1124864, 1225043

Offset: 0

N. J. A. Sloane

Also the perfect cubes with digital root 8. [Proof: perfect cubes are either of the form (3n)^3 or of the form (3n+1)^3 or of the form (3n+2)^3. These subsets have digital root 9, 1 and 8 respectively.] - R. J. Mathar, Oct 02 2008

			a(4) = (3*4 + 2)^3 = 2744.
a(8) = (3*8 + 2)^3 = 17576.

Amarnath Murthy, Fabricating a perfect cube with a given valid digit sum (to be published)

Harry J. Smith, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Cf. A054966, A016779, A016789, A073636.

(3*Range[0,40]+2)^3 (* or *) LinearRecurrence[{4,-6,4,-1},{8,125,512,1331},40] (* Harvey P. Dale, Feb 20 2013 *)

a(n) = { (3*n + 2)^3 } \\ Harry J. Smith, Jul 18 2009

a(n) = A016789(n)^3. - Nathaniel Johnston, May 04 2011
G.f.: (8 + 93*x + 60*x^2 + x^3)/(1 - 4*x + 6*x^2 - 4*x^3 + x^4). - Colin Barker, Jan 02 2012
a(0)=8, a(1)=125, a(2)=512, a(3)=1331, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Harvey P. Dale, Feb 20 2013
Sum_{n>=0} 1/a(n) = -2*Pi^3 / (81*sqrt(3)) + 13*zeta(3)/27. - Amiram Eldar, Oct 02 2020

More terms from Harry J. Smith, Jul 18 2009

First digital root in proof in comment line corrected. - Ant King, May 01 2013

A016935 a(n) = (6*n + 2)^3.

Original entry on oeis.org

8, 512, 2744, 8000, 17576, 32768, 54872, 85184, 125000, 175616, 238328, 314432, 405224, 512000, 636056, 778688, 941192, 1124864, 1331000, 1560896, 1815848, 2097152, 2406104, 2744000, 3112136

Offset: 0

N. J. A. Sloane

The generating function is 8 times the g.f. of A016779. - R. J. Mathar, May 07 2008

			a(1) = (6*1 + 2)^3 = 8^3 = 512.

Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Cf. A002117, A016779, A016911, A016923, A016933, A016959, A016971.

[(6*n+2)^3: n in [0..50]]; // Vincenzo Librandi, May 04 2011

(6*Range[0,30]+2)^3 (* or *) LinearRecurrence[{4,-6,4,-1},{8,512,2744,8000},30] (* Harvey P. Dale, Aug 23 2019 *)

a(n) = 8*A016779(n). - R. J. Mathar, May 07 2008
Sum_{n>=0} 1/a(n) = Pi^3 / (324*sqrt(3)) + 13*zeta(3)/216. - Amiram Eldar, Oct 02 2020
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Wesley Ivan Hurt, Oct 02 2020
G.f.: 8*(1+60*x+93*x^2+8*x^3)/(-1+x)^4. - Wesley Ivan Hurt, Oct 02 2020

A016780 a(n) = (3*n+1)^4.

Original entry on oeis.org

1, 256, 2401, 10000, 28561, 65536, 130321, 234256, 390625, 614656, 923521, 1336336, 1874161, 2560000, 3418801, 4477456, 5764801, 7311616, 9150625, 11316496, 13845841, 16777216, 20151121, 24010000, 28398241, 33362176, 38950081, 45212176, 52200625, 59969536, 68574961

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 (5,-10,10,-5,1).

Cf. A000583 (n^4), A016777 (3n+1), A016778, A016779, A016781.

[(3*n+1)^4: n in [0..30]]; // Vincenzo Librandi, Sep 21 2011

(3*Range[0,30]+1)^4 (* or *) LinearRecurrence[{5,-10,10,-5,1},{1,256,2401,10000,28561},30] (* Harvey P. Dale, Oct 21 2015 *)

From Harvey P. Dale, Oct 21 2015: (Start)
a(n) = 5*a(n-1) -10*a(n-2) +10*a(n-3) -5*a(n-4) +a(n-5).
G.f.: -((1+251*x+1131*x^2+545*x^3+16*x^4)/(-1+x)^5). (End)
a(n) = A000583(A016777(n)). - Michel Marcus, Nov 06 2015
E.g.f.: exp(x)*(1+255*x+945*x^2+594*x^3+81*x^4). - Wolfdieter Lang, Apr 02 2017
Sum_{n>=0} 1/a(n) = PolyGamma(3, 1/3)/486. - Amiram Eldar, Mar 29 2022

A016781 a(n) = (3*n+1)^5.

Original entry on oeis.org

1, 1024, 16807, 100000, 371293, 1048576, 2476099, 5153632, 9765625, 17210368, 28629151, 45435424, 69343957, 102400000, 147008443, 205962976, 282475249, 380204032, 503284375, 656356768, 844596301, 1073741824, 1350125107, 1680700000, 2073071593, 2535525376

Offset: 0

N. J. A. Sloane

In general the e.g.f. of {(1 + 3*m)^n}{m>=0} is E(n,x) = exp(x)*Sum{m=0..n} A282629(n, m)*x^m, and the o.g.f. is G(n, x) = (Sum_{m=0..n} A225117(n, n-m)*x^m)/(1-x)^(n+1). - Wolfdieter Lang, Apr 02 2017

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Cf. A016777, A016778, A016779, A016780, A225117, A282629.

[(3*n+1)^5: n in [0..30]]; // Vincenzo Librandi, Sep 21 2011

(3Range[0,20]+1)^5 (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{1,1024,16807,100000,371293,1048576},30] (* Harvey P. Dale, May 13 2012 *)

A016781(n):=(3*n+1)^5$
makelist(A016781(n),n,0,20); /* Martin Ettl, Nov 12 2012 */

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, May 13 2012
From Wolfdieter Lang, Apr 02 2017: (Start)
O.g.f.: (1+1018*x+10678*x^2+14498*x^3+2933*x^4+32*x^5)/(1-x)^6.
E.g.f: exp(x)*(1+1023*x+7380*x^2+8775*x^3+2835*x^4+243*x^5). (End)
a(n) = A000584(A016777(n)). - Michel Marcus, Apr 06 2017
Sum_{n>=0} 1/a(n) = 2*Pi^5/(3^6*sqrt(3)) + 121*zeta(5)/3^5. - Amiram Eldar, Mar 29 2022

A016782 a(n) = (3*n+1)^6.

Original entry on oeis.org

1, 4096, 117649, 1000000, 4826809, 16777216, 47045881, 113379904, 244140625, 481890304, 887503681, 1544804416, 2565726409, 4096000000, 6321363049, 9474296896, 13841287201, 19770609664, 27680640625, 38068692544, 51520374361, 68719476736, 90458382169, 117649000000

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 (7,-21,35,-35,21,-7,1).

Cf. A001014, A016777, A016778, A016779, A016780, A016781.

[(3*n+1)^6: n in [0..30]]; // Vincenzo Librandi, Sep 21 2011

Table[(3n+1)^6,{n,0,100}] (* Mohammad K. Azarian, Jun 15 2016 *)
LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,4096,117649,1000000,4826809,16777216,47045881},20] (* Harvey P. Dale, Sep 30 2016 *)

a(n) = A001014(A016777(n)). - Michel Marcus, Jun 15 2016
From Ilya Gutkovskiy, Jun 15 2016: (Start)
G.f.: (1 + 4089*x + 88998*x^2 + 262438*x^3 + 154113*x^4 + 15177*x^5 + 64*x^6)/(1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7). (End)
Sum_{n>=0} 1/a(n) = PolyGamma(5, 1/3)/87480. - Amiram Eldar, Mar 29 2022

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

Original entry on oeis.org

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

cp's OEIS Frontend

A061102 Duplicate of A016779.

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A016777 a(n) = 3*n + 1.

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A016778 a(n) = (3*n+1)^2.

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A016791 a(n) = (3*n + 2)^3.

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A016935 a(n) = (6*n + 2)^3.

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A016780 a(n) = (3*n+1)^4.

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A016781 a(n) = (3*n+1)^5.

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