A140504 -id:A140504 - cp's OEIS frontend

A028399 a(n) = 2^n - 4.

0, 4, 12, 28, 60, 124, 252, 508, 1020, 2044, 4092, 8188, 16380, 32764, 65532, 131068, 262140, 524284, 1048572, 2097148, 4194300, 8388604, 16777212, 33554428, 67108860, 134217724, 268435452, 536870908, 1073741820, 2147483644, 4294967292, 8589934588, 17179869180

Offset: 2

N. J. A. Sloane

Number of permutations of [n] with 2 sequences.
Number of 2 X n binary matrices that avoid simultaneously the right angled numbered polyomino patterns (ranpp) (00;1) and (11;0). An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1Sergey Kitaev, Nov 11 2004
The number of edges in the dual Edwards-Venn diagram graph with n-1 digits when n>2.
a(n) (n>=6) is the number of vertices in the molecular graph NS2[n-5], defined pictorially in the Ashrafi et al. reference (Fig. 2, where NS2[2] is shown). - Emeric Deutsch, May 16 2018
From Petros Hadjicostas, Aug 08 2019: (Start)
With regard to the comment above about a(n) being the "number of permutations of [n] with 2 sequences", we refer to Ex. 13 (pp. 260-261) of Comtet (1974), who uses the definition of a "séquence" given by André in several of his papers in the 19th century.
In the terminology of array A059427, these so-called "séquences" in permutations (defined by Comtet and André) are called "alternating runs" (or just "runs"). We discuss these so-called "séquences" below.
If b = (b_1, b_2, ..., b_n) is a permutation of [n], written in one-line notation (not in cycle notation), a "séquence" in a permutation of length l >= 2 (according to Comtet) is a maximal interval of integers {i, i+1, ..., i+l-1} for some i (where 1 <= i <= n-l+1) such that b_i < b_{i+1} < ... < b_{i+l-1} or b_i > b_{i+1} > ... > b_{i+l-1}. (The word "maximal" means that, in the first case, we have b_{i-1} > b_i and b_{i+l} < b_{i+l-1}, while in the second case, we have b_{i-1} < b_i and b_{i+l} > b_{i+l-1} provided b_{i-1} and b_{i+l} can be defined.)
When defining a "séquence", André (1884) actually refers to the list of terms (b_i, b_{i+1}, ..., b_{i+l-1}) rather than the corresponding index set {i, i+1, ..., i+l-1} (which is essentially the same thing).
For more details about these so-called "séquences" (or "alternate runs"), see the comments and examples for sequence A000708.
(End)
For n >= 1, a(n+2) is the number of shortest paths from (0,0) of a square grid to {(x,y): |x|+|y| = n} along the grid line. - Jianing Song, Aug 23 2021

			From _Petros Hadjicostas_, Aug 08 2019: (Start)
We have a(3) = 4 because each of the following permutations of [3] has the following so-called "séquences" ("alternate runs"):
   123 -> 123 (one),
   132 -> 13, 32 (two),
   213 -> 21, 13 (two),
   231 -> 23, 31 (two),
   312 -> 31, 12 (two),
   321 -> 321 (one).
Recall that a so-called "séquence" ("alternate run") must start with a "maximum" and end with "minimum", or vice versa, and it should not contain any other maxima and minima in between. Two consecutive such "séquences" ("alternate runs") have exactly one minimum or exactly one maximum in common.
(End)

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 261.
A. W. F. Edwards, Cogwheels of the Mind, Johns Hopkins University Press, 2004, p. 82.

Muniru A Asiru, Table of n, a(n) for n = 2..700
Désiré André, Sur les permutations alternées, J. Math. Pur. Appl., 7 (1881), 167-184.
Désiré André, Étude sur les maxima, minima et séquences des permutations, Ann. Sci. Ecole Norm. Sup., 3, no. 1 (1884), 121-135.
Désiré André, Mémoire sur les permutations quasi-alternées, Journal de mathématiques pures et appliquées 5e série, tome 1 (1895), 315-350.
Désiré André, Mémoire sur les séquences des permutations circulaires, Bulletin de la S. M. F., tome 23 (1895), pp. 122-184.
Ali Reza Ashrafi and Parisa Nikzad, Kekulé index and bounds of energy for nanostar dendrimers, Digest J. of Nanomaterials and Biostructures, 4, No. 2, 2009, 383-388.
Sergey Kitaev, On multi-avoidance of right angled numbered polyomino patterns, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.
Sergey Kitaev, On multi-avoidance of right angled numbered polyomino patterns, University of Kentucky Research Reports (2004).
László Németh, Pascal pyramid in the space H^2 x R, arXiv:1701.06022 [math.CO], 2017 (3rd line of Table 2 is a(n+1)).
I. Strazdins, Universal affine classification of Boolean functions, Acta Applic. Math. 46 (1997), 147-167.
Index entries for linear recurrences with constant coefficients, signature (3,-2).

Column k = 2 of A059427.
Row n = 2 of A371064.
Cf. A000225, A000918, A052548, A140504, A175164.
Cf. A000203, A003945.

a:=List([2..40], n->2^n-4); # Muniru A Asiru, May 17 2018

seq(2^n-4, n=2..40); # Muniru A Asiru, May 17 2018

2^Range[2,40]-4 (* Harvey P. Dale, Jul 05 2019 *)

PARI
```
a(n)=if(n<2, 0, 2^n-4)
```

def A028399(n): return (1<Chai Wah Wu, Jun 27 2023

O.g.f.: 4*x^3/((1-x)*(1-2*x)). - R. J. Mathar, Aug 07 2008
From Reinhard Zumkeller, Feb 28 2010: (Start)
a(n) = A175164(2*n)/A140504(n+2);
a(2*n) = A052548(n)*A000918(n) for n > 0;
a(n) = A173787(n,2). (End)
a(n) = a(n-1) + 2^(n-1) (with a(2)=0). - Vincenzo Librandi, Nov 22 2010
a(n) = 4*A000225(n-2). - R. J. Mathar, Dec 15 2015
E.g.f.: 3 + 2*x - 4*exp(x) + exp(2*x). - Stefano Spezia, Apr 06 2021
a(n) = sigma(A003945(n-2)) for n>=3. - Flávio V. Fernandes, Apr 20 2021

Additional comments from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Dec 02 2001

A057168 Next larger integer with same binary weight (number of 1 bits) as n.

Original entry on oeis.org

2, 4, 5, 8, 6, 9, 11, 16, 10, 12, 13, 17, 14, 19, 23, 32, 18, 20, 21, 24, 22, 25, 27, 33, 26, 28, 29, 35, 30, 39, 47, 64, 34, 36, 37, 40, 38, 41, 43, 48, 42, 44, 45, 49, 46, 51, 55, 65, 50, 52, 53, 56, 54, 57, 59, 67, 58, 60, 61, 71, 62, 79, 95, 128, 66, 68, 69, 72, 70, 73, 75

Offset: 1

Marc LeBrun, Sep 14 2000

Binary weight is given by A000120.

			a(6)=9 since 6 has two one-bits (i.e., 6=2+4) and 9 is the next higher integer of binary weight two (7 is weight three and 8 is weight one).

Donald Knuth, The Art of Computer Programming, Vol. 4A, section 7.1.3, exercises 20-21.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
M. Beeler, R. W. Gosper, and R. Schroeppel, HAKMEM, MIT Artificial Intelligence Laboratory, Memo AIM-239, February 1972, Item 175 by Gosper, page 81. Also HTML transcription.
Donald E. Knuth, The Art of Computer Programming, Pre-Fascicle 1A, Draft of Section 7.1.3, 2008. Exercises 20 and 21 page 54 and answers pages 75-76.
Marc B. Reynolds, Popcount walks: next, previous, toward and nearest (2023)

Cf. A000120, A006519, A057169, A000051, A052548, A140504, A000225, A055010, A007283, A171942.

Cf. A000079, A018900, A014311, A014312, A014313, A023688, A023689, A023690, A023691 (Hamming weight = 1, 2, ..., 9).

a057168 n = a057168_list !! (n-1)
a057168_list = f 2 $ tail a000120_list where
   f x (z:zs) = (x + length (takeWhile (/= z) zs)) : f (x + 1) zs
-- Reinhard Zumkeller, Aug 26 2012

a[n_] := (bw = DigitCount[n, 2, 1]; k = n+1; While[ DigitCount[k, 2, 1] != bw, k++]; k); Table[a[n], {n, 1, 71}](* Jean-François Alcover, Nov 28 2011 *)

a(n)=my(u=bitand(n,-n),v=u+n);(bitxor(v,n)/u)>>2+v \\ Charles R Greathouse IV, Oct 28 2009

A057168(n)=n+bitxor(n,n+n=bitand(n,-n))\n\4+n \\ M. F. Hasler, Aug 27 2014

def a(n): u = n&-n; v = u+n; return (((v^n)//u)>>2)+v
print([a(n) for n in range(1, 72)]) # Michael S. Branicky, Jul 10 2022 after Charles R Greathouse IV

def A057168(n): return ((n&~(b:=n+(a:=n&-n)))>>a.bit_length())^b # Chai Wah Wu, Mar 06 2025

From Reinhard Zumkeller, Aug 18 2008: (Start)
a(A000079(n)) = A000079(n+1);
a(A000051(n)) = A052548(n);
a(A052548(n)) = A140504(n);
a(A000225(n)) = A055010(n);
a(A007283(n)) = A000051(n+2). (End)
a(n) = MIN{m: A000120(m)=A000120(n) and m>n}. - Reinhard Zumkeller, Aug 15 2009
For k,m>0, a((2^k-1)*2^m) = 2^(k+m)+2^(k-1)-1. - Chai Wah Wu, Mar 07 2025
If n is odd, then a(n) = XOR(n,OR(a,a/2)) where a = AND(-n,n+1). - Chai Wah Wu, Mar 08 2025

A173786 Triangle read by rows: T(n,k) = 2^n + 2^k, 0 <= k <= n.

Original entry on oeis.org

2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 17, 18, 20, 24, 32, 33, 34, 36, 40, 48, 64, 65, 66, 68, 72, 80, 96, 128, 129, 130, 132, 136, 144, 160, 192, 256, 257, 258, 260, 264, 272, 288, 320, 384, 512, 513, 514, 516, 520, 528, 544, 576, 640, 768, 1024, 1025, 1026, 1028, 1032, 1040, 1056, 1088, 1152, 1280, 1536, 2048

Offset: 0

Reinhard Zumkeller, Feb 28 2010

Essentially the same as A048645. - T. D. Noe, Mar 28 2011

			Triangle begins as:
     2;
     3,    4;
     5,    6,    8;
     9,   10,   12,   16;
    17,   18,   20,   24,   32;
    33,   34,   36,   40,   48,   64;
    65,   66,   68,   72,   80,   96,  128;
   129,  130,  132,  136,  144,  160,  192,  256;
   257,  258,  260,  264,  272,  288,  320,  384,  512;
   513,  514,  516,  520,  528,  544,  576,  640,  768, 1024;
  1025, 1026, 1028, 1032, 1040, 1056, 1088, 1152, 1280, 1536, 2048;

T. D. Noe, Rows n = 0..100 of triangle, flattened
Wawrzyniec Bieniawski, Piotr Masierak, Andrzej Tomski, and Szymon Łukaszyk, Assembly Theory - Formalizing Assembly Spaces and Discovering Patterns and Bounds, Preprints.org (2025).

Cf. A048645, A118413, A118416.

Cf. also A087112, A370121.

[2^n + 2^k: k in [0..n], n in [0..12]]; // G. C. Greubel, Jul 07 2021

Flatten[Table[2^n + 2^m, {n,0,10}, {m, 0, n}]] (* T. D. Noe, Jun 18 2013 *)

A173786(n) = { my(c = (sqrtint(8*n + 1) - 1) \ 2); 1 << c + 1 << (n - binomial(c + 1, 2)); }; \\ Antti Karttunen, Feb 29 2024, after David A. Corneth's PARI-program in A048645

from math import isqrt, comb
def A173786(n):
    a = (m:=isqrt(k:=n+1<<1))-(k<=m*(m+1))
    return (1<Chai Wah Wu, Jun 20 2025

flatten([[2^n + 2^k for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jul 07 2021

1 <= A000120(T(n,k)) <= 2.
For n>0, 0<=kA048645(n+1,k+2) and T(n,n) = A048645(n+2,1).
Row sums give A006589(n).
Central terms give A161168(n).
T(2*n+1,n) = A007582(n+1).
T(2*n+1,n+1) = A028403(n+1).
T(n,k) = A140513(n,k) - A173787(n,k), 0<=k<=n.
T(n,k) = A059268(n+1,k+1) + A173787(n,k), 0T(n,k) * A173787(n,k) = A173787(2*n,2*k), 0<=k<=n.
T(n,0) = A000051(n).
T(n,1) = A052548(n) for n>0.
T(n,2) = A140504(n) for n>1.
T(n,3) = A175161(n-3) for n>2.
T(n,4) = A175162(n-4) for n>3.
T(n,5) = A175163(n-5) for n>4.
T(n,n-4) = A110287(n-4) for n>3.
T(n,n-3) = A005010(n-3) for n>2.
T(n,n-2) = A020714(n-2) for n>1.
T(n,n-1) = A007283(n-1) for n>0.
T(n,n) = 2*A000079(n).

Typo in first comment line fixed by Reinhard Zumkeller, Mar 07 2010

A244673 Numbers k that divide 2^k + 4.

Original entry on oeis.org

1, 2, 3, 4, 20, 260, 740, 2132, 2180, 5252, 43364, 49268, 49737, 80660, 130052, 293620, 542852, 661412, 717027, 865460, 1564180, 2185220, 2192132, 2816372, 3784916, 4377620, 4427540, 5722004, 6307652, 6919460, 8765252, 9084452, 9498260, 9723611, 11346260, 12208820, 12220132

Offset: 1

Derek Orr, Jul 14 2014

nonn

			2^2 + 4 = 8 is divisible by 2. Thus 2 is a term of this sequence.
2^3 + 4 = 12 is divisible by 3. Thus 3 is a term of this sequence.
2^4 + 4 = 20 is divisible by 4. Thus 4 is a term of this sequence.

Jens Kruse Andersen, Table of n, a(n) for n = 1..100
OEIS Wiki, 2^n mod n

The odd terms form A115976.

Cf. A015921, A140504.

A244673:=n->`if`(type((2^n+4)/n, integer), n, NULL): seq(A244673(n), n=1..10^5); # Wesley Ivan Hurt, Jul 15 2014
Alternative:
select(n -> 4 + 2&^n mod n = 0, [$1..10^5]); # Robert Israel, Jul 15 2014

Select[Range[1000], Mod[2^# + 4, #] == 0 &] (* Alonso del Arte, Jul 14 2014 *)
Join[{1,2,3},Select[Range[1223*10^4],PowerMod[2,#,#]==#-4&]] (* Harvey P. Dale, Jan 16 2023 *)

for(n=1, 10^8, if(Mod(2,n)^n+4==0, print1(n, ", "))) \\ Jens Kruse Andersen, Jul 15 2014

A175161 a(n) = 8*(2^n + 1).

Original entry on oeis.org

16, 24, 40, 72, 136, 264, 520, 1032, 2056, 4104, 8200, 16392, 32776, 65544, 131080, 262152, 524296, 1048584, 2097160, 4194312, 8388616, 16777224, 33554440, 67108872, 134217736, 268435464, 536870920, 1073741832, 2147483656, 4294967304, 8589934600, 17179869192

Offset: 0

Reinhard Zumkeller, Feb 28 2010

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2).

Sequences of the form m*(2^n + 1): A000051 (m=1), A052548 (m=2), A140504 (m=4), A153973 (m=6), A231643 (m=5), this sequence (m=8), A175162 (m=16), A175163 (m=32).

Cf. A159741, A173786, A175166.

I:=[16,24]; [n le 2 select I[n] else 3*Self(n-1) - 2*Self(n-2): n in [1..41]]; // G. C. Greubel, Jul 08 2021

8*(2^Range[0, 40] + 1) (* G. C. Greubel, Jul 08 2021 *)
LinearRecurrence[{3,-2},{16,24},40] (* Harvey P. Dale, Feb 10 2022 *)

[8*(2^n +1) for n in (0..40)] # G. C. Greubel, Jul 08 2021

a(n) = A173786(n+3, 3).
a(n) = A175166(2*n)/A159741(n) for n > 0.
a(n) = 3*a(n-1) -2*a(n-2) with a(0)=16, a(1)=24. - Vincenzo Librandi, Dec 28 2010
G.f.: 8*(2 - 3*x)/((1-x)*(1-2*x)). - Chai Wah Wu, Jun 20 2020
a(n) = 8 * A000051(n). - Alois P. Heinz, Jun 20 2020
E.g.f.: 8*(exp(2*x) + exp(x)). - G. C. Greubel, Jul 08 2021

A175164 a(n) = 16*(2^n - 1).

Original entry on oeis.org

0, 16, 48, 112, 240, 496, 1008, 2032, 4080, 8176, 16368, 32752, 65520, 131056, 262128, 524272, 1048560, 2097136, 4194288, 8388592, 16777200, 33554416, 67108848, 134217712, 268435440

Offset: 0

Reinhard Zumkeller, Feb 28 2010

nonn

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2).

Sequences of the form m*(2^n - 1): A000225 (m=1), A000918 (m=2), A068156 (m=3), A028399 (m=4), A068293 (m=6), A159741 (m=8), this sequence (m=16), A175165 (m=32), A175166 (m=64).

Cf. A140504, A173787.

I:=[0,16]; [n le 2 select I[n] else 3*Self(n-1) - 2*Self(n-2): n in [1..41]]; // G. C. Greubel, Jul 08 2021

16*(2^Range[0,40] - 1) (* G. C. Greubel, Jul 08 2021 *)

def A175164(n): return (1<Chai Wah Wu, Jun 27 2023

[16*(2^n -1) for n in (0..40)] # G. C. Greubel, Jul 08 2021

a(n) = 2^(n+4) - 16.
a(n) = A173787(n+4, 4).
a(2*n) = A140504(n+2)*A028399(n).
a(n) = 3*a(n-1) - 2*a(n-2), a(0)=0, a(1)=16. - Vincenzo Librandi, Dec 28 2010
From G. C. Greubel, Jul 08 2021: (Start)
G.f.: 16*x/((1-x)*(1-2*x)).
E.g.f.: 16*(exp(2*x) - exp(x)). (End)

A175162 a(n) = 16*(2^n + 1).

Original entry on oeis.org

32, 48, 80, 144, 272, 528, 1040, 2064, 4112, 8208, 16400, 32784, 65552, 131088, 262160, 524304, 1048592, 2097168, 4194320, 8388624, 16777232, 33554448, 67108880, 134217744, 268435472, 536870928, 1073741840, 2147483664, 4294967312, 8589934608, 17179869200

Offset: 0

Reinhard Zumkeller, Feb 28 2010

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2).

Sequences of the form m*(2^n + 1): A000051 (m=1), A052548 (m=2), A140504 (m=4), A153973 (m=6), A231643 (m=5), A175161 (m=8), this sequence (m=16), A175163 (m=32).

Cf. A173786.

I:=[32,48]; [n le 2 select I[n] else 3*Self(n-1) - 2*Self(n-2): n in [1..41]]; // G. C. Greubel, Jul 08 2021

16*(2^Range[0,30] +1) (* or *) LinearRecurrence[{3,-2},{32,48},30] (* Harvey P. Dale, Jun 08 2017 *)

[16*(2^n +1) for n in (0..40)] # G. C. Greubel, Jul 08 2021

a(n) = A173786(n+4, 4).
a(n) = 3*a(n-1) - 2*a(n-2), a(0)=32, a(1)=48. - Vincenzo Librandi, Dec 28 2010
From G. C. Greubel, Jul 08 2021: (Start)
G.f.: 16*(2 - 3*x)/((1-x)*(1-2*x)).
E.g.f.: 16*(exp(2*x) + exp(x)). (End)

A175163 a(n) = 32*(2^n + 1).

Original entry on oeis.org

64, 96, 160, 288, 544, 1056, 2080, 4128, 8224, 16416, 32800, 65568, 131104, 262176, 524320, 1048608, 2097184, 4194336, 8388640, 16777248, 33554464, 67108896, 134217760, 268435488, 536870944

Offset: 0

Reinhard Zumkeller, Feb 28 2010

nonn

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2).

Sequences of the form m*(2^n + 1): A000051 (m=0), A052548 (m=2), A140504 (m=4), A153973 (m=6), A231643 (m=5), A175161 (m=8), A175162 (m=16), this sequence (m=32).

Cf. A173786.

I:=[64,96]; [n le 2 select I[n] else 3*Self(n-1) - 2*Self(n-2): n in [1..41]]; // G. C. Greubel, Jul 08 2021

32*(2^Range[0,40] + 1) (* G. C. Greubel, Jul 08 2021 *)

[32*(2^n +1) for n in (0..40)] # G. C. Greubel, Jul 08 2021

a(n) = A173786(n+5, 5).
a(n) = 3*a(n-1) - 2*a(n-2), a(0)=64, a(1)=96. - Vincenzo Librandi, Dec 28 2010
G.f.: 32*(2 - 3*x)/((1 - x)*(1 - 2*x)). - Chai Wah Wu, Jul 24 2020
E.g.f.: 32*(exp(2*x) + exp(x)). - G. C. Greubel, Jul 08 2021

A254365 a(n) = 2^(n+2) + 3^n + 10.

Original entry on oeis.org

15, 21, 35, 69, 155, 381, 995, 2709, 7595, 21741, 63155, 185349, 547835, 1627101, 4848515, 14479989, 43308875, 129664461, 388469075, 1164358629, 3490978715, 10468741821, 31397836835, 94176733269, 282496645355, 847422827181, 2542134263795, 7626134355909

Offset: 0

Luciano Ancora, Jan 29 2015

This is the sequence of third terms of "fourth partial sums of m-th powers".

Colin Barker, Table of n, a(n) for n = 0..1000
Luciano Ancora, Demonstration of formulas, page 1.
Luciano Ancora, Recurrence relations for partial sums of m-th powers
Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

Cf. A140504, A254366, A254367.

Table[2^(n+2) + 3^n + 10, {n, 0, 30}] (* Bruno Berselli, Jan 30 2015 *)

vector(30, n, n--; 2^(n+2) + 3^n + 10) \\ Colin Barker, Jan 30 2015

G.f.: -(74*x^2-69*x+15) / ((x-1)*(2*x-1)*(3*x-1)). - Colin Barker, Jan 30 2015

a(n) = 6*a(n-1)-11*a(n-2)+6*a(n-3). - Colin Barker, Jan 30 2015

A254366 a(n) = 4^n + 102^n + 43^n + 20.

Original entry on oeis.org

35, 56, 112, 272, 760, 2336, 7672, 26432, 94360, 346016, 1295032, 4923392, 18943960, 73568096, 287731192, 1131465152, 4467809560, 17697740576, 70271780152, 279532195712, 1113469251160, 4439908895456, 17717752225912, 70745400779072, 282604862628760

Offset: 0

Luciano Ancora, Jan 29 2015

This is the sequence of fourth terms of "fourth partial sums of m-th powers".

Colin Barker, Table of n, a(n) for n = 0..1000
Luciano Ancora, Demonstration of formulas, page 2.
Luciano Ancora, Recurrence relations for partial sums of m-th powers
Index entries for linear recurrences with constant coefficients, signature (10,-35,50,-24).

Cf. A140504, A254365, A254367.

Table[4^n + 10*2^n + 4*3^n + 20, {n, 0, 28}] (* Michael De Vlieger, Jan 30 2015 *)

vector(30, n, n--; 4^n + 10*2^n + 4*3^n + 20) \\ Colin Barker, Jan 30 2015

G.f.: -(638*x^3-777*x^2+294*x-35) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)). - Colin Barker, Jan 30 2015

a(n) = 10*a(n-1)-35*a(n-2)+50*a(n-3)-24*a(n-4). - Colin Barker, Jan 30 2015

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cp's OEIS Frontend

A028399 a(n) = 2^n - 4.

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A057168 Next larger integer with same binary weight (number of 1 bits) as n.

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A173786 Triangle read by rows: T(n,k) = 2^n + 2^k, 0 <= k <= n.

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A244673 Numbers k that divide 2^k + 4.

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A175161 a(n) = 8*(2^n + 1).

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A175164 a(n) = 16*(2^n - 1).

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A254366 a(n) = 4^n + 102^n + 43^n + 20.