A001021 -id:A001021 - cp's OEIS frontend

A066006 Sum of digits of 12^n.

1, 3, 9, 18, 18, 27, 45, 36, 54, 45, 45, 54, 54, 63, 81, 72, 90, 72, 81, 117, 108, 90, 99, 99, 117, 117, 135, 153, 135, 135, 153, 180, 153, 117, 117, 180, 171, 171, 189, 198, 216, 198, 225, 225, 216, 198, 225, 234, 252, 234, 216, 234, 279, 243

Offset: 0

N. J. A. Sloane, Dec 11 2001

Harry J. Smith, Table of n, a(n) for n = 0..1000

Cf. sum of digits of k^n: A001370 (k=2), A004166 (k=3), A065713 (k=4), A066001 (k=5), A066002 (k=6), A066003(k=7), A066004 (k=8), A065999 (k=9), A066005 (k=11), this sequence (k=12), A175527 (k=13).

Table[Total[IntegerDigits[12^n]], {n, 0, 60}] (* Vincenzo Librandi, Oct 08 2013 *)

a(n) = sumdigits(12^n); \\ Michel Marcus, Nov 01 2013

a(n) = A007953(A001021(n)). - Michel Marcus, Nov 01 2013

A081142 12th binomial transform of (0,0,1,0,0,0,...).

Original entry on oeis.org

0, 0, 1, 36, 864, 17280, 311040, 5225472, 83607552, 1289945088, 19349176320, 283787919360, 4086546038784, 57954652913664, 811365140791296, 11234286564802560, 154070215745863680, 2095354934143746048

Offset: 0

Paul Barry, Mar 08 2003

Starting at 1, the three-fold convolution of A001021 (powers of 12).

Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (36,-432,1728).

Cf. A001021.

Sequences similar to the form q^(n-2)*binomial(n, 2): A000217 (q=1), A001788 (q=2), A027472 (q=3), A038845 (q=4), A081135 (q=5), A081136 (q=6), A027474 (q=7), A081138 (q=8), A081139 (q=9), A081140 (q=10), A081141 (q=11), this sequence (q=12), A027476 (q=15).

List([0..20],n->12^(n-2)*Binomial(n,2)); # Muniru A Asiru, Nov 24 2018

[12^(n-2)* Binomial(n, 2): n in [0..20]]; // Vincenzo Librandi, Oct 16 2011

seq(coeff(series(x^2/(1-12*x)^3,x,n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Nov 24 2018

LinearRecurrence[{36,-432,1728},{0,0,1},30] (* or *) Table[(n-1) (n-2) 3^(n-3) 2^(2n-7),{n,20}] (* Harvey P. Dale, Jul 25 2013 *)

vector(20, n, n--; 2^(2*n-5)*3^(n-2)*n*(n-1)) \\ G. C. Greubel, Nov 23 2018

[2^(2*n-5)*3^(n-2)*n*(n-1) for n in range(20)] # G. C. Greubel, Nov 23 2018

a(n) = 36*a(n-1) - 432*a(n-2) + 1728*a(n-3), a(0) = a(1) = 0, a(2) = 1.
a(n) = 12^(n-2)*binomial(n, 2).
G.f.: x^2/(1 - 12*x)^3.
a(n) = 2^(2*n-5)*3^(n-2)*n*(n-1). - Harvey P. Dale, Jul 25 2013
E.g.f.: (1/2)*exp(12*x)*x^2. - Franck Maminirina Ramaharo, Nov 23 2018
From Amiram Eldar, Jan 06 2022: (Start)
Sum_{n>=2} 1/a(n) = 24 - 264*log(12/11).
Sum_{n>=2} (-1)^n/a(n) = 312*log(13/12) - 24. (End)

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

A008572 Digits of powers of 12.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

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

			Triangle begins:
  1;
  1, 2;
  1, 4, 4;
  1, 7, 2, 8;
  2, 0, 7, 3, 6;
  2, 4, 8, 8, 3, 2;
  2, 9, 8, 5, 9, 8, 4;
  ...

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. A001021.

Cf. A000455, A008564, A008565, A008566, A008567, A008568, A008569, A008570, A008571, A008573, A010054.

Flatten[IntegerDigits/@(12^Range[0,15])] (* Harvey P. Dale, Dec 19 2011 *)

A212165 Numbers k such that the maximum exponent in its prime factorization is not less than the number of positive exponents (A051903(k) >= A001221(k)).

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 16, 17, 18, 19, 20, 23, 24, 25, 27, 28, 29, 31, 32, 36, 37, 40, 41, 43, 44, 45, 47, 48, 49, 50, 52, 53, 54, 56, 59, 61, 63, 64, 67, 68, 71, 72, 73, 75, 76, 79, 80, 81, 83, 88, 89, 92, 96, 97, 98, 99, 100, 101, 103, 104

Offset: 1

Matthew Vandermast, May 22 2012

Union of A212164 and A212166.  Includes numerous subsequences that are subsequences of neither A212164 nor A212166.
Includes all factorials except A000142(3) = 6.
Observation: all terms in DATA section are also the first 65 numbers n whose difference between the arithmetic derivative of n and the sum of the divisors of n is nonnegative. - Omar E. Pol, Dec 19 2012

			10 = 2^1*5^1 has 2 distinct prime factors, hence, 2 positive exponents in its prime factorization (although 1s are often left implicit).  2 is larger than the maximal exponent in 10's prime factorization, which is 1. Therefore, 10 does not belong to the sequence. But 20 = 2^2*5^1 and 40 = 2^3*5^1 belong, since the largest exponents in their prime factorizations are 2 and 3 respectively.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 844.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Primefan, The First 2500 Integers Factored (first of 5 pages).

Complement of A212168.
See also A212167.
Subsequences (none of which are subsequences of A212164 or A212166) include A000079, A001021, A066120, A087980, A130091, A141586, A166475, A181818, A181823, A181824, A182763, A212169. Also includes all terms in A181813 and A181814.
Cf. A001221, A051903, A188654, A225230.

import Data.List (findIndices)
a212165 n = a212165_list !! (n-1)
a212165_list = map (+ 1) $ findIndices (<= 0) a225230_list
-- Reinhard Zumkeller, May 03 2013

okQ[n_] := Module[{f = Transpose[FactorInteger[n]][[2]]}, Max[f] >= Length[f]]; Select[Range[1000], okQ] (* T. D. Noe, May 24 2012 *)

is(k) = {my(e = factor(k)[, 2]); !(#e) || vecmax(e) >= #e;} \\ Amiram Eldar, Sep 08 2024

A225230(a(n)) <= 0. - Reinhard Zumkeller, May 03 2013

A223233 T(n,k)=Rolling icosahedron footprints: number of nXk 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an icosahedral edge.

Original entry on oeis.org

1, 5, 12, 25, 65, 144, 125, 785, 845, 1728, 625, 7445, 25225, 10985, 20736, 3125, 75665, 492365, 812225, 142805, 248832, 15625, 753005, 11043445, 32837285, 26157625, 1856465, 2985984, 78125, 7540985, 236027705, 1697263985, 2191464605, 842416625

Offset: 1

R. H. Hardin Mar 18 2013

Table starts
............1.............5................25.................125
...........12............65...............785................7445
..........144...........845.............25225..............492365
.........1728.........10985............812225............32837285
........20736........142805..........26157625..........2191464605
.......248832.......1856465.........842416625........146259564725
......2985984......24134045.......27130395625.......9761484584045
.....35831808.....313742585......873746350625.....651489782832965
....429981696....4078653605....28139386665625...43480983274973885
...5159780352...53022496865...906241361740625.2901957882023749205
..61917364224..689292459245.29185902861015625
.743008370688.8960801970185

			Some solutions for n=3 k=4
..0..6..0..5....0..5..6..5....0..7..0..1....0..1..3..1....0..1..0..7
..0..6.10..5....0..5..6..5....3..7..0..7....3..7..3..9....0..7..0..7
..0..5.10..4....6..2..6..5....3..7..5..7....3..9.11..7....3..1..3..7
Vertex neighbors:
0 -> 1 2 5 6 7
1 -> 0 2 3 7 8
2 -> 0 1 4 6 8
3 -> 1 7 8 9 11
4 -> 2 6 8 9 10
5 -> 0 6 7 10 11
6 -> 0 2 4 5 10
7 -> 0 1 3 5 11
8 -> 1 2 3 4 9
9 -> 3 4 8 10 11
10 -> 4 5 6 9 11
11 -> 3 5 7 9 10

R. H. Hardin, Table of n, a(n) for n = 1..97

Column 1 is A001021(n-1)
Column 2 is 5*13^(n-1)
Row 1 is A000351(n-1)

Empirical for column k:
k=1: a(n) = 12*a(n-1)
k=2: a(n) = 13*a(n-1)
k=3: a(n) = 35*a(n-1) -90*a(n-2)
k=4: a(n) = 73*a(n-1) -423*a(n-2) +351*a(n-3)
k=5: [order 11]
k=6: [order 26]
Empirical for row n:
n=1: a(n) = 5*a(n-1)
n=2: a(n) = 7*a(n-1) +30*a(n-2) for n>3
n=3: a(n) = 18*a(n-1) +103*a(n-2) -552*a(n-3) +540*a(n-4) for n>5
n=4: a(n) = [order 12] for n>13

A024140 a(n) = 12^n - 1.

Original entry on oeis.org

0, 11, 143, 1727, 20735, 248831, 2985983, 35831807, 429981695, 5159780351, 61917364223, 743008370687, 8916100448255, 106993205379071, 1283918464548863, 15407021574586367, 184884258895036415

Offset: 0

N. J. A. Sloane

In base 12 these are 0, B, BB, BBB, ... . - David Rabahy, Dec 12 2016

Index entries for linear recurrences with constant coefficients, signature (13,-12).

Cf. A001021, A016125, A178248.

Cf. Similar sequences of the type k^n-1: A000004 (k=1), A000225 (k=2), A024023 (k=3), A024036 (k=4), A024049 (k=5), A024062 (k=6), A024075 (k=7), A024088 (k=8), A024101 (k=9), A002283 (k=10), A024127 (k=11), this sequence (k=12).

12^Range[0,20]-1 (* or *) LinearRecurrence[{13,-12},{0,11},20] (* Harvey P. Dale, Feb 01 2019 *)

From Mohammad K. Azarian, Jan 14 2009: (Start)
G.f.: 1/(1-12*x) - 1/(1-x).
E.g.f.: exp(12*x) - exp(x). (End)
a(n) = 12*a(n-1) + 11 for n>0, a(0)=0. - Vincenzo Librandi, Nov 18 2010
a(n) = Sum_{i=1..n} 11^i*binomial(n,n-i) for n>0, a(0)=0. - Bruno Berselli, Nov 11 2015
From Elmo R. Oliveira, Dec 15 2023: (Start)
a(n) = 13*a(n-1) - 12*a(n-2) for n>1.
a(n) = A001021(n)-1 = A178248(n)-2.
a(n) = 11*(A016125(n) - 1)/12. (End)

A090042 a(n) = 2a(n-1) + 11a(n-2) for n > 1, a(0) = a(1) = 1.

Original entry on oeis.org

1, 1, 13, 37, 217, 841, 4069, 17389, 79537, 350353, 1575613, 7005109, 31341961, 139740121, 624241813, 2785624957, 12437909857, 55517694241, 247852396909, 1106399430469, 4939175226937, 22048744189033, 98428415874373, 439393017828109, 1961498610274321, 8756320416657841

Offset: 0

Paul Barry, Nov 20 2003

Binomial transform of A001021 (powers of 12), with interpolated zeros.
For n > 0, a(n) = term (1,1) in the n-th power of the 2 X 2 matrix [1,3; 4,1]. - Gary W. Adamson, Aug 06 2010
a(n) is the number of compositions of n when there are 1 type of 1 and 12 types of other natural numbers. - Milan Janjic, Aug 13 2010

Muniru A Asiru, Table of n, a(n) for n = 0..319
Index entries for sequences related to Chebyshev polynomials.
Index entries for linear recurrences with constant coefficients, signature (2,11).

Cf. A049310, A015520, A084603.

a := [1, 1];; for n in [3..30] do a[n] := 2*a[n-1]+ 11*a[n-2]; od; a; # Muniru A Asiru, Feb 18 2018

I:=[1,1]; [n le 2 select I[n] else 2*Self(n-1) +11*Self(n-2): n in [1..30]]; // G. C. Greubel, Aug 02 2019

a := proc(n) option remember: if n=0 then 1 elif n=1 then 1 elif n>=2 then 2*procname(n-1) + 11*procname(n-2) fi; end:
seq(a(n), n=0..25); # Muniru A Asiru, Feb 18 2018

a[n_]:= Simplify[((1+Sqrt[12])^n +(1-Sqrt[12])^n)/2]; Array[a, 30, 0] (* or *)
CoefficientList[Series[(x-1)/(11x^2+2x-1), {x,0,30}], x] (* or *)
Table[ MatrixPower[{{1, 2}, {6, 1}}, n][[1, 1]], {n, 0, 30}] (* Robert G. Wilson v, Sep 18 2013 and modified per Wolfdieter Lang Feb 17 2018 *)
LinearRecurrence[{2, 11}, {1, 1}, 30] (* Ray Chandler, Aug 01 2015 *)

x='x+O('x^30); Vec((1-x)/(1-2*x-11*x^2)) \\ Altug Alkan, Feb 17 2018

((1-x)/(1-2*x-11*x^2)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Aug 02 2019

E.g.f.: exp(x)*cosh(2*sqrt(3)*x).
a(n) = ((1 + 2*sqrt(3))^n + (1 - 2*sqrt(3))^n)/2.
a(n) = Sum_{k=0..n} A098158(n,k)*12^(n-k). - Philippe Deléham, Dec 26 2007
If p[1]=1, and p[i]=12, (i>1), and if A is Hessenberg matrix of order n defined by: A[i,j]=p[j-i+1], (i<=j), A[i,j]=-1, (i=j+1), and A[i,j]=0 otherwise. Then, for n>=1, a(n)=det A. - Milan Janjic, Apr 29 2010
From Wolfdieter Lang, Feb 17 2018: (Start)
G.f.: (1-x)/(1 - 2*x - 11*x^2). (See the Mathematica program.)
a(n) = b(n+1) - b(n), with b(n) = A015520(n). This leads to the Binet-de Moivre type formula given in the Mathematica program.
a(n) = (i*sqrt(11))^n*(S(n,-2*i/sqrt(11)) + (i/sqrt(11))*S(n-1,-2*i/sqrt(11))), n >= 0, with Chebyshev S polynomials (coefficients in A049310), with S(-2, x) = -1, S(-1, x) = 0 and i = sqrt(-1). Via Cayley-Hamilton. See the Gary W. Adamson comment above or the Mathematica program of Robert G. Wilson v with another matrix. (End)
From Peter Bala, Jan 07 2022: (Start)
a(n) = [x^n] (x + sqrt(1 + 12*x^2))^n.
The Gauss congruences a(n*p^k) == a(n^p^(k-1)) (mod p^k) hold for prime p and positive integers n and k.
O.g.f.: 1 + x*d/dx(log(B(x))), where B(x) = 1/sqrt(1 - 2*x - 11*x^2) is the o.g.f. of A084603. (End)

A223321 T(n,k)=Rolling icosahedron footprints: number of nXk 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge.

Original entry on oeis.org

1, 5, 12, 25, 125, 144, 125, 1625, 3125, 1728, 625, 21125, 105625, 78125, 20736, 3125, 274625, 3570125, 6865625, 1953125, 248832, 15625, 3570125, 122039125, 603351125, 446265625, 48828125, 2985984, 78125, 46411625, 4176940625, 54279694625

Offset: 1

R. H. Hardin Mar 19 2013

Table starts
........1...........5..............25................125....................625
.......12.........125............1625..............21125.................274625
......144........3125..........105625............3570125..............122039125
.....1728.......78125.........6865625..........603351125............54279694625
....20736.....1953125.......446265625.......101966340125.........24143758634125
...248832....48828125.....29007265625.....17232311481125......10739266230499625
..2985984..1220703125...1885472265625...2912260640310125....4776881955584279125
.35831808.30517578125.122555697265625.492172048212411125.2124782217358970404625

			Some solutions for n=3 k=4
..0..1..8..9....0..1..0..7....0..1..0..2....0..1..0..6....0..6..2..4
..0..2..8..2....0..5..0..5....0..6..0..2....0..6.10..5....0..1..2..4
..6..2..4..2....0..1..0..7....0..7..0..7....0..6.10..5....0..6.10..4
Vertex neighbors:
0 -> 1 2 5 6 7
1 -> 0 2 3 7 8
2 -> 0 1 4 6 8
3 -> 1 7 8 9 11
4 -> 2 6 8 9 10
5 -> 0 6 7 10 11
6 -> 0 2 4 5 10
7 -> 0 1 3 5 11
8 -> 1 2 3 4 9
9 -> 3 4 8 10 11
10 -> 4 5 6 9 11
11 -> 3 5 7 9 10

R. H. Hardin, Table of n, a(n) for n = 1..97

Column 1 is A001021(n-1)
Column 2 is A013710(n-1)
Column 3 is 25*65^(n-1)
Column 4 is 125*169^(n-1)
Row 1 is A000351(n-1)

Empirical for column k:
k=1: a(n) = 12*a(n-1)
k=2: a(n) = 25*a(n-1)
k=3: a(n) = 65*a(n-1)
k=4: a(n) = 169*a(n-1)
k=5: a(n) = 479*a(n-1) -15210*a(n-2)
k=6: a(n) = 1366*a(n-1) -232713*a(n-2) +9253764*a(n-3)
k=7: [order 8]
Empirical for row n:
n=1: a(n) = 5*a(n-1)
n=2: a(n) = 13*a(n-1) for n>2
n=3: a(n) = 38*a(n-1) -129*a(n-2) for n>4
n=4: [order 7] for n>10
n=5: [order 32] for n>36

A033048 Sums of distinct powers of 12.

Original entry on oeis.org

0, 1, 12, 13, 144, 145, 156, 157, 1728, 1729, 1740, 1741, 1872, 1873, 1884, 1885, 20736, 20737, 20748, 20749, 20880, 20881, 20892, 20893, 22464, 22465, 22476, 22477, 22608, 22609, 22620, 22621, 248832, 248833, 248844, 248845, 248976

Offset: 0

Clark Kimberling

Numbers without any base-12 digits greater than 1.

T. D. Noe, Table of n, a(n) for n = 0..1023
Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Identities and periodic oscillations of divide-and-conquer recurrences splitting at half, arXiv:2210.10968 [cs.DS], 2022, p. 45.
Eric Weisstein's World of Mathematics, Duodecimal
Wikipedia, Duodecimal

Subsequence of A102487.
Cf. A000695, A005836, A033042-A033052.
Row 11 of array A104257.

import Data.List (unfoldr)
a033048 n = a033048_list !! (n-1)
a033048_list = filter (all (< 2) . unfoldr (\x ->
   if x == 0 then Nothing else Just $ swap $ divMod x 12)) [1..]
-- Reinhard Zumkeller, Apr 17 2011

With[{k = 12}, Map[FromDigits[#, k] &, Tuples[{0, 1}, 6]]] (* Michael De Vlieger, Oct 28 2022 *)

{maxn=37;
for(vv=0,maxn,
bvv=binary(vv);
ll=length(bvv);texp=0;btod=0;
forstep(i=ll,1,-1,btod=btod+bvv[i]*12^texp;texp++);
print1(btod,", "))}
\\ Douglas Latimer, Apr 16 2012

a(n)=fromdigits(binary(n),12) \\ Charles R Greathouse IV, Jan 11 2017

a(n) = Sum_{i=0..m} d(i)*12^i, where Sum_{i=0..m} d(i)*2^i is the base-2 representation of n.
a(n) = A097258(n)/11.
a(2n) = 12*a(n), a(2n+1) = a(2n)+1.
a(n) = Sum_{k>=0} A030308(n,k)*b(k) with b(k) = 12^k = A001021(k). - Philippe Deléham, Oct 19 2011
G.f.: (1/(1 - x))*Sum_{k>=0} 12^k*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jun 04 2017

Extended by Ray Chandler, Aug 03 2004

cp's OEIS Frontend

A066006 Sum of digits of 12^n.

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A081142 12th binomial transform of (0,0,1,0,0,0,...).

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

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A008572 Digits of powers of 12.

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A212165 Numbers k such that the maximum exponent in its prime factorization is not less than the number of positive exponents (A051903(k) >= A001221(k)).

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A223233 T(n,k)=Rolling icosahedron footprints: number of nXk 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an icosahedral edge.

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A024140 a(n) = 12^n - 1.

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A090042 a(n) = 2a(n-1) + 11a(n-2) for n > 1, a(0) = a(1) = 1.