A000400 -id:A000400 - cp's OEIS frontend

A223504 T(n,k)=Petersen graph (3,1) coloring a rectangular array: number of nXk 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.

1, 3, 6, 9, 19, 36, 27, 115, 121, 216, 81, 631, 1519, 771, 1296, 243, 3539, 16323, 20115, 4913, 7776, 729, 19759, 182901, 426359, 266419, 31307, 46656, 2187, 110427, 2030665, 9685063, 11148439, 3528715, 199497, 279936, 6561, 617015, 22598167

Offset: 1

R. H. Hardin Mar 21 2013

Table starts
........1........3............9..............27.................81
........6.......19..........115.............631...............3539
.......36......121.........1519...........16323.............182901
......216......771........20115..........426359............9685063
.....1296.....4913.......266419........11148439..........515473927
.....7776....31307......3528715.......291545903........27465794119
....46656...199497.....46737819......7624417031......1463848507173
...279936..1271251....619042315....199391762123.....78024299447333
..1679616..8100769...8199214219...5214442630935...4158831849750231
.10077696.51620379.108598575915.136366781617267.221674060909378867

			Some solutions for n=3 k=4
..0..3..4..1....0..2..1..4....0..3..0..3....0..2..1..2....0..1..4..3
..0..3..4..3....5..2..5..4....4..1..0..1....1..2..0..2....0..1..0..3
..5..3..0..1....1..2..1..2....0..1..0..1....5..2..0..2....0..3..0..1

R. H. Hardin, Table of n, a(n) for n = 1..199

Column 1 is A000400(n-1)
Column 2 is A138977
Row 1 is A000244(n-1)

Empirical for column k:
k=1: a(n) = 6*a(n-1)
k=2: a(n) = 7*a(n-1) -4*a(n-2)
k=3: a(n) = 15*a(n-1) -24*a(n-2) +10*a(n-3)
k=4: a(n) = 31*a(n-1) -127*a(n-2) -20*a(n-3) +705*a(n-4) -1027*a(n-5) +499*a(n-6) -60*a(n-7)
k=5: [order 21]
k=6: [order 53]
Empirical for row n:
n=1: a(n) = 3*a(n-1)
n=2: a(n) = 5*a(n-1) +4*a(n-2) -4*a(n-3) for n>4
n=3: a(n) = 12*a(n-1) -4*a(n-2) -73*a(n-3) +103*a(n-4) -23*a(n-5) -16*a(n-6) +4*a(n-7) for n>8
n=4: [order 21] for n>22
n=5: [order 60] for n>61

A240523 a(n) = floor(4^n/((1+sqrt(5))/2)^(2*n)).

Original entry on oeis.org

1, 1, 2, 3, 5, 8, 12, 19, 29, 45, 69, 105, 161, 247, 377, 577, 881, 1347, 2058, 3144, 4805, 7341, 11216, 17137, 26183, 40005, 61122, 93387, 142682, 218000, 333074, 508892, 777518, 1187942, 1815014, 2773095, 4236913

Offset: 0

Kival Ngaokrajang, Apr 07 2014

a(n) is the perimeter (rounded down) of pentaflake after n iterations, let a(0) = 1. The total number of sides is 5*A000302(n).

G. C. Greubel, Table of n, a(n) for n = 0..1000
Kival Ngaokrajang, Illustration for n = 0..4
Eric Weisstein's World of Mathematics, Pentaflake
Wikipedia, n-flake

Cf. A000302, A000400, A113212.

A240523:=n->floor(4^n/((1+sqrt(5))/2)^(2*n)); seq(A240523(n), n=0..50); # Wesley Ivan Hurt, Apr 07 2014

Table[Floor[4^n/(((1 + Sqrt[5]))/2)^(2 n)], {n, 0, 50}] (* Wesley Ivan Hurt, Apr 07 2014 *)
Table[Floor[4^n/GoldenRatio^(2n)],{n,0,40}] (* Harvey P. Dale, Mar 24 2018 *)

PARI
```
a(n) = floor(4^n/((1+sqrt(5))/2)^(2*n))
```

Equals floor((2/(phi))^(2*n)), where phi is the golden ratio. - G. C. Greubel, Jul 05 2017

A322827 A permutation of A025487: Sequence of least representatives of distinct prime signatures obtained from the run lengths present in the binary expansion of n.

Original entry on oeis.org

1, 2, 6, 4, 36, 30, 12, 8, 216, 180, 210, 900, 72, 60, 24, 16, 1296, 1080, 1260, 5400, 44100, 2310, 6300, 27000, 432, 360, 420, 1800, 144, 120, 48, 32, 7776, 6480, 7560, 32400, 264600, 13860, 37800, 162000, 9261000, 485100, 30030, 5336100, 1323000, 69300, 189000, 810000, 2592, 2160, 2520, 10800, 88200, 4620, 12600

Offset: 0

Antti Karttunen, Jan 16 2019

A101296(a(n)) gives a permutation of natural numbers.

			The sequence can be represented as a binary tree:
                                      1
                                      |
                   ...................2...................
                  6                                       4
       36......../ \........30                 12......../ \........8
       / \                 / \                 / \                 / \
      /   \               /   \               /   \               /   \
     /     \             /     \             /     \             /     \
   216      180         210    900         72       60         24       16
etc.
Both children are multiples of their common parent, see A323503, A323504 and A323507.
The value of a(n) is computed from the binary expansion of n as follows: Starting from the least significant end of the binary expansion of n (A007088), we record the successive run lengths, subtract one from all lengths except the first one, and use the reversed partial sums of these adjusted values as the exponents of successive primes.
For 11, which is "1011" in base 2, we have run lengths [2, 1, 1] when scanned from the right, and when one is subtracted from all except the first, we have [2, 0, 0], partial sums of which is [2, 2, 2], which stays same when reversed, thus a(11) = 2^2 * 3^2 * 5^2 = 900.
For 13, which is "1101" in base 2, we have run lengths [1, 1, 2] when scanned from the right, and when one is subtracted from all except the first, we have [1, 0, 1], partial sums of which is [1, 1, 2], reversed [2, 1, 1], thus a(13) = 2^2 * 3^1 * 5^1 = 60.
Sequence A227183 is based on the same algorithm.

Antti Karttunen, Table of n, a(n) for n = 0..16383
Index entries for sequences related to binary expansion of n

Cf. A000079 (right edge), A000400 (left edge, apart from 2), A005811, A046523, A101296, A227183, A322585, A322825, A323503, A323504, A323507.
Other rearrangements of A025487 include A036035, A059901, A063008, A077569, A085988, A086141, A087443, A108951, A181821, A181822.
Cf. A005940, A283477, A323505 for other similar trees.

{1}~Join~Array[Times @@ MapIndexed[Prime[First@ #2]^#1 &, Reverse@ Accumulate@ MapIndexed[Length[#1] - Boole[First@ #2 > 1] &, Split@ Reverse@ IntegerDigits[#, 2]]] &, 54] (* Michael De Vlieger, Feb 05 2020 *)

A322827(n) = if(!n,1,my(bits = Vecrev(binary(n)), rl=1, o = List([])); for(i=2,#bits,if(bits[i]==bits[i-1], rl++, listput(o,rl))); listput(o,rl); my(es=Vecrev(Vec(o)), m=1); for(i=1,#es,m *= prime(i)^es[i]); (m));

a(n) = A046523(a(n)) = A046523(A322825(n)).
A001221(a(n)) = A005811(n).
A001222(a(n)) = A227183(n).
A322585(a(n)) = 1.

A008567 Digits of powers of 6.

Original entry on oeis.org

1, 6, 3, 6, 2, 1, 6, 1, 2, 9, 6, 7, 7, 7, 6, 4, 6, 6, 5, 6, 2, 7, 9, 9, 3, 6, 1, 6, 7, 9, 6, 1, 6, 1, 0, 0, 7, 7, 6, 9, 6, 6, 0, 4, 6, 6, 1, 7, 6, 3, 6, 2, 7, 9, 7, 0, 5, 6, 2, 1, 7, 6, 7, 8, 2, 3, 3, 6, 1, 3, 0, 6, 0, 6, 9, 4, 0, 1, 6, 7, 8, 3, 6, 4, 1, 6, 4, 0, 9, 6, 4, 7, 0, 1, 8, 4, 9, 8, 4

Offset: 0

N. J. A. Sloane

Irregular table with row length sequence A210436. - Jason Kimberley, Nov 26 2012

The constant whose decimal expansion is this sequence is irrational (Mahler, 1981). - Amiram Eldar, Mar 23 2025

			Triangle begins:
  1;
  6;
  3, 6;
  2, 1, 6;
  1, 2, 9, 6;
  7, 7, 7, 6;
  4, 6, 6, 5, 6;
  2, 7, 9, 9, 3, 6;
  1, 6, 7, 9, 6, 1, 6;
  1, 0, 0, 7, 7, 6, 9, 6;
  ...

Seiichi Manyama, Rows n = 0..100, flattened
Kurt Mahler, On some irrational decimal fractions, Journal of Number Theory, Vol. 13, No. 2 (1981), pp. 268-269.

Cf. A000400, A210436.

Cf. A000455, A008564, A008565, A008566, A008568, A008569, A008570, A008571, A008572, A008573, A010054.

A009992 Powers of 48: a(n) = 48^n.

Original entry on oeis.org

1, 48, 2304, 110592, 5308416, 254803968, 12230590464, 587068342272, 28179280429056, 1352605460594688, 64925062108545024, 3116402981210161152, 149587343098087735296, 7180192468708211294208, 344649238497994142121984, 16543163447903718821855232

Offset: 0

N. J. A. Sloane

Same as Pisot sequences E(1, 48), L(1, 48), P(1, 48), T(1, 48). Essentially same as Pisot sequences E(48, 2304), L(48, 2304), P(48, 2304), T(48, 2304). See A008776 for definitions of Pisot sequences.
If X_1, X_2, ..., X_n is a partition of the set {1,2,...,2*n} into blocks of size 2 then, for n>=1, a(n) is equal to the number of functions f : {1,2,..., 2*n}->{1,2,3,4,5,6,7} such that for fixed y_1,y_2,...,y_n in {1,2,3,4,5,6,7} we have f(X_i)<>{y_i}, (i=1,2,...,n). - Milan Janjic, May 24 2007
The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n >= 1, a(n) equals the number of 48-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

T. D. Noe, Table of n, a(n) for n = 0..100
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (48).

Cf. A001018 (powers of 8), ..., A001029 (powers of 19), A009964 (powers of 20), ..., A009991 (powers of 47), A087752 (powers of 49).

Cf. A000079 (2^n), A000244 (3^n), A000302 (4^n), A000400 (6^n), A001018 (8^n), A001021 (12^n), A001025 (16^n), A009968 (24^n).

List([0..20],n->48^n); # Muniru A Asiru, Nov 21 2018

[48^n: n in [0..20]] // Vincenzo Librandi, Nov 21 2010

A009992 := n -> 48^n: seq(A009992(n), n=0..20); # M. F. Hasler, Apr 19 2015

48^Range[0, 15] (* Michael De Vlieger, Jan 13 2018 *)

A009992(n)=48^n \\ M. F. Hasler, Apr 19 2015

for n in range(0,20): print(48**n, end=', ') # Stefano Spezia, Nov 21 2018

[(48)^n for n in range(20)] # G. C. Greubel, Nov 21 2018

G.f.: 1/(1-48*x). - Philippe Deléham, Nov 24 2008
a(n) = 48^n; a(n) = 48*a(n-1), a(0)=1. - Vincenzo Librandi, Nov 21 2010
E.g.f.: exp(48*x). - Muniru A Asiru, Nov 21 2018

Edited by M. F. Hasler, Apr 19 2015

A038221 Triangle whose (i,j)-th entry is binomial(i,j)3^(i-j)3^j.

Original entry on oeis.org

1, 3, 3, 9, 18, 9, 27, 81, 81, 27, 81, 324, 486, 324, 81, 243, 1215, 2430, 2430, 1215, 243, 729, 4374, 10935, 14580, 10935, 4374, 729, 2187, 15309, 45927, 76545, 76545, 45927, 15309, 2187, 6561, 52488, 183708, 367416, 459270, 367416, 183708, 52488, 6561

Offset: 0

N. J. A. Sloane

Triangle of coefficients in expansion of (3 + 3x)^n = 3^n (1 +x)^n, where n is a nonnegative integer. (Coefficients in expansion of (1 +x)^n are given in A007318: Pascal's triangle). - Zagros Lalo, Jul 23 2018

			Triangle begins as:
     1;
     3,     3;
     9,    18,      9;
    27,    81,     81,     27;
    81,   324,    486,    324,     81;
   243,  1215,   2430,   2430,   1215,    243;
   729,  4374,  10935,  14580,  10935,   4374,    729;
  2187, 15309,  45927,  76545,  76545,  45927,  15309,  2187;
  6561, 52488, 183708, 367416, 459270, 367416, 183708, 52488, 6561;

Shara Lalo and Zagros Lalo, Polynomial Expansion Theorems and Number Triangles, Zana Publishing, 2018, ISBN: 978-1-9995914-0-3, pp. 44, 48

Indranil Ghosh, Rows 0..100 of triangle, flattened
B. N. Cyvin et al., Isomer enumeration of unbranched catacondensed polygonal systems with pentagons and heptagons, Match, No. 34 (Oct 1996), pp. 109-121.

Cf. A007318, A304236, A304249.
Cf. A000007, A000400, A027465, A030195, A057083.
Columns k: A000244 (k=0), 3*A027471 (k=1), 3^2*A027472 (k=2), 3^3*A036216 (k=3), 3^4*A036217 (k=4), 3^5*A036219 (k=5), 3^6*A036220 (k=6), 3^7*A036221 (k=7), 3^8*A036222 (k=8), 3^9*A036223 (k=9), 3^10*A172362 (k=10).

Flat(List([0..8],i->List([0..i],j->Binomial(i,j)*3^(i-j)*3^j))); # Muniru A Asiru, Jul 23 2018

a038221 n = a038221_list !! n
a038221_list = concat $ iterate ([3,3] *) [1]
instance Num a => Num [a] where
   fromInteger k = [fromInteger k]
   (p:ps) + (q:qs) = p + q : ps + qs
   ps + qs         = ps ++ qs
   (p:ps) * qs'@(q:qs) = p * q : ps * qs' + [p] * qs
    *                = []
-- Reinhard Zumkeller, Apr 02 2011

[3^n*Binomial(n,k): k in [0..n], n in [0..10]]; // G. C. Greubel, Oct 17 2022

(* programs from Zagros Lalo, Jul 23 2018 *)
t[0, 0]=1; t[n_, k_]:= t[n, k]= If[n<0 || k<0, 0, 3 t[n-1, k] + 3 t[n-1, k-1]]; Table[t[n, k], {n,0,10}, {k,0,n}]//Flatten
Table[CoefficientList[Expand[3^n *(1+x)^n], x], {n,0,10}]//Flatten
Table[3^n Binomial[n, k], {n,0,10}, {k,0,n}]//Flatten  (* End *)

def A038221(n,k): return 3^n*binomial(n,k)
flatten([[A038221(n,k) for k in range(n+1)] for n in range(10)]) # G. C. Greubel, Oct 17 2022

G.f.: 1/(1 - 3*x - 3*x*y). - Ilya Gutkovskiy, Apr 21 2017
T(0,0) = 1; T(n,k) = 3 T(n-1,k) + 3 T(n-1,k-1) for k = 0...n; T(n,k)=0 for n or k < 0. - Zagros Lalo, Jul 23 2018
From G. C. Greubel, Oct 17 2022: (Start)
T(n, k) = T(n, n-k).
T(n, n) = A000244(n).
T(n, n-1) = 3*A027471(n).
T(n, n-2) = 9*A027472(n+1).
T(n, n-3) = 27*A036216(n-3).
T(n, n-4) = 81*A036217(n-4).
T(n, n-5) = 243*A036219(n-5).
Sum_{k=0..n} T(n, k) = A000400(n).
Sum_{k=0..n} (-1)^k * T(n, k) = A000007(n).
Sum_{k=0..floor(n/2)} T(n-k, k) = A030195(n+1), n >= 0.
Sum_{k=0..floor(n/2)} (-1)^k * T(n-k, k) = A057083(n).
T(n, k) = 3^k * A027465(n, k). (End)

A067411 Third column of triangle A067410 and second column of A067417.

Original entry on oeis.org

1, 4, 24, 144, 864, 5184, 31104, 186624, 1119744, 6718464, 40310784, 241864704, 1451188224, 8707129344, 52242776064, 313456656384, 1880739938304, 11284439629824, 67706637778944, 406239826673664

Offset: 0

Wolfdieter Lang, Jan 25 2002

Let f(k) be the sum of the smallest three positive divisors of k, g(k) be the sum of the largest two positive divisors of k, this sequence from a(2) onwards contains the numbers k for which g(k) is a positive integer power of f(k). - Yifan Xie, Jan 27 2024

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Paul Barry and A. Hennessy, The Euler-Seidel Matrix, Hankel Matrices and Moment Sequences, J. Int. Seq. 13 (2010) # 10.8.2, Example 14.
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Craig Knecht, Number of tilings for a stackable six sphinx tile shape.
Index entries for linear recurrences with constant coefficients, signature (6).

A002001, A067412 (second and fourth column of A067410), A000244, A067403 (first and third column of A067417), A000400 (powers of 6).

Row sums of A038195.

CoefficientList[Series[(1-2x)/(1-6x),{x,0,30}],x] (* Harvey P. Dale, Feb 26 2015 *)

a(n) = if(n<=0, 0, 4*6^(n-1) ); \\ Joerg Arndt, Feb 23 2014

a(n) = A067410(n+2, 2) = A067417(n+1, 1).
a(n) = 4 * 6^(n-1), for n >= 1, a(0)=1.
G.f.: (1-2*x)/(1-6*x).
E.g.f.: (2*exp(6*x)+1) / 3 = exp(3*x)*(cosh(3*x) + sinh(3*x)/3). - Paul Barry, Nov 20 2003
a(n) = Sum_{k=0..n} C(n,k) * A001045(n+k+1). - Paul Barry, Apr 19 2010

Incorrect formula deleted by Harvey P. Dale, Feb 26 2015

Formula restored by Sean A. Irvine, Jan 10 2021

A223269 T(n,k)=Rolling cube face footprints: number of nXk 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across a corresponding cube edge.

Original entry on oeis.org

1, 4, 6, 16, 48, 36, 64, 576, 576, 216, 256, 6144, 20992, 6912, 1296, 1024, 67584, 622592, 765952, 82944, 7776, 4096, 737280, 19726336, 63438848, 27951104, 995328, 46656, 16384, 8060928, 611319808, 5889851392, 6467616768, 1020002304, 11943936

Offset: 1

R. H. Hardin Mar 19 2013

Table starts
....1......4.........16...........64.............256...............1024
....6.....48........576.........6144...........67584.............737280
...36....576......20992.......622592........19726336..........611319808
..216...6912.....765952.....63438848......5889851392.......522106961920
.1296..82944...27951104...6467616768...1771674009600....450204914417664
.7776.995328.1020002304.659411697664.534392715870208.389343801904201728

			Some solutions for n=3 k=4
..0..3..1..2....0..1..0..1....0..4..5..1....0..4..2..4....0..2..1..3
..0..2..4..3....0..3..5..1....0..4..0..3....0..1..0..4....0..3..4..2
..4..2..1..2....0..2..0..1....3..1..5..4....3..4..0..1....0..3..4..0
Face neighbors:
0.->.1.2.3.4
1.->.0.2.3.5
2.->.0.1.4.5
3.->.0.1.4.5
4.->.0.3.2.5
5.->.1.3.4.2

R. H. Hardin, Table of n, a(n) for n = 1..311

Column 1 is A000400(n-1)
Column 2 is 4*12^(n-1)
Column 3 is A223197
Row 1 is A000302(n-1)

Empirical for column k:
k=1: a(n) = 6*a(n-1)
k=2: a(n) = 12*a(n-1)
k=3: a(n) = 40*a(n-1) -128*a(n-2)
k=4: a(n) = 112*a(n-1) -1024*a(n-2)
k=5: [order 6]
k=6: [order 9]
k=7: [order 19]
Empirical for row n:
n=1: a(n) = 4*a(n-1)
n=2: a(n) = 8*a(n-1) +32*a(n-2)
n=3: a(n) = 24*a(n-1) +256*a(n-2) -1024*a(n-3) for n>4
n=4: [order 6] for n>7
n=5: [order 10] for n>11
n=6: [order 23] for n>24

A223556 T(n,k)=Petersen graph (3,1) coloring a rectangular array: number of nXk 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.

Original entry on oeis.org

1, 3, 6, 9, 27, 36, 27, 171, 243, 216, 81, 1089, 3249, 2187, 1296, 243, 6939, 44217, 61731, 19683, 7776, 729, 44217, 609309, 1795473, 1172889, 177147, 46656, 2187, 281763, 8410671, 53599905, 72906921, 22284891, 1594323, 279936, 6561, 1795473

Offset: 1

R. H. Hardin Mar 22 2013

Table starts
........1..........3.............9...............27...................81
........6.........27...........171.............1089.................6939
.......36........243..........3249............44217...............609309
......216.......2187.........61731..........1795473.............53599905
.....1296......19683.......1172889.........72906921...........4715559621
.....7776.....177147......22284891.......2960456193.........414863325945
....46656....1594323.....423412929.....120212193177.......36498667573629
...279936...14348907....8044845651....4881332621169.....3211064180380305
..1679616..129140163..152852067369..198211242377097...282501632829717621
.10077696.1162261467.2904189280011.8048559615522273.24853807982558115945

			Some solutions for n=3 k=4
..0..3..5..2....0..1..4..1....0..2..5..2....0..2..5..2....0..1..2..0
..5..3..0..1....0..1..0..3....1..2..5..2....5..2..1..4....2..0..1..2
..4..3..4..3....2..1..4..5....0..2..0..1....1..2..1..2....1..4..5..3

R. H. Hardin, Table of n, a(n) for n = 1..219

Column 1 is A000400(n-1)
Column 2 is A013708(n-1)
Column 3 = 9*19^(n-1) is row 8 of A223556 with T(2+,3) = A121057(8,1+)
Row 1 is A000244(n-1)

Empirical for column k:
k=1: a(n) = 6*a(n-1)
k=2: a(n) = 9*a(n-1)
k=3: a(n) = 19*a(n-1)
k=4: a(n) = 41*a(n-1) -16*a(n-2)
k=5: a(n) = 95*a(n-1) -626*a(n-2) +720*a(n-3) for n>4
k=6: [order 8] for n>9
k=7: [order 13] for n>15
Empirical for row n:
n=1: a(n) = 3*a(n-1)
n=2: a(n) = 7*a(n-1) -4*a(n-2) for n>3
n=3: a(n) = 17*a(n-1) -47*a(n-2) +41*a(n-3) -10*a(n-4) for n>6
n=4: [order 13] for n>16
n=5: [order 41] for n>45

A224012 T(n,k)=Number of nXk 0..2 arrays with rows nondecreasing and antidiagonals unimodal.

Original entry on oeis.org

3, 6, 9, 10, 36, 27, 15, 100, 216, 81, 21, 225, 868, 1296, 243, 28, 441, 2661, 7378, 7776, 729, 36, 784, 6815, 28541, 62764, 46656, 2187, 45, 1296, 15340, 90051, 297859, 534352, 279936, 6561, 55, 2025, 31324, 245055, 1108969, 3094127, 4549684, 1679616

Offset: 1

R. H. Hardin Mar 30 2013

Table starts
.....3........6.........10..........15...........21............28............36
.....9.......36........100.........225..........441...........784..........1296
....27......216........868........2661.........6815.........15340.........31324
....81.....1296.......7378.......28541........90051........245055........595822
...243.....7776......62764......297859......1108969.......3516324.......9866389
...729....46656.....534352.....3094127.....13275381......47735665.....150787422
..2187...279936....4549684....32148473....157347899.....630339756....2200064042
..6561..1679616...38737252...334179881...1859567103....8213689391...31256208954
.19683.10077696..329817976..3474343713..21962353421..106375878027..437370837827
.59049.60466176.2808146488.36122604265.259365424097.1373916879120.6067995150599

			Some solutions for n=3 k=4
..1..1..2..2....0..1..1..1....0..0..0..0....0..0..0..1....0..2..2..2
..0..2..2..2....0..1..1..1....0..1..2..2....2..2..2..2....0..0..1..1
..1..1..2..2....0..2..2..2....1..2..2..2....2..2..2..2....0..0..2..2

R. H. Hardin, Table of n, a(n) for n = 1..449

Column 1 is A000244
Column 2 is A000400
Row 1 is A000217(n+1)
Row 2 is A000537(n+1)

Empirical: columns k=1..7 have recurrences of order 1,1,5,7,11,14,19

Empirical: rows n=1..7 are polynomials of degree 2*n for k>0,0,1,2,3,4,5

cp's OEIS Frontend

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A240523 a(n) = floor(4^n/((1+sqrt(5))/2)^(2*n)).

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A322827 A permutation of A025487: Sequence of least representatives of distinct prime signatures obtained from the run lengths present in the binary expansion of n.

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A008567 Digits of powers of 6.

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A009992 Powers of 48: a(n) = 48^n.

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A038221 Triangle whose (i,j)-th entry is binomial(i,j)*3^(i-j)*3^j.

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A067411 Third column of triangle A067410 and second column of A067417.

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A038221 Triangle whose (i,j)-th entry is binomial(i,j)3^(i-j)3^j.