A020714 -id:A020714 - cp's OEIS frontend

A336101 Numbers divisible by exactly one odd prime.

3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 31, 34, 36, 37, 38, 40, 41, 43, 44, 46, 47, 48, 49, 50, 52, 53, 54, 56, 58, 59, 61, 62, 67, 68, 71, 72, 73, 74, 76, 79, 80, 81, 82, 83, 86, 88, 89, 92, 94, 96, 97, 98, 100, 101, 103, 104

Offset: 1

Peter Munn, Jul 08 2020

Numbers k for which A001221(A000265(k)) = 1. - Antti Karttunen, Jul 08 2020
Numbers whose odd part is a prime power (A246655). - Amiram Eldar, Jul 08 2020
Numbers of the form 2^r * p^q  with p an odd prime (A065091), r >= 0, q >= 1. - Bernard Schott, Dec 14 2020

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000265, A001221, A246655, A340373 (characteristic function).
Positions of ones in A005087.
Subsequence of A267895.
Subsequences: A007283 (3*2^n), A020714 (5*2^n), A005009 (7*2^n), A005015 (11*2^n), A005029 (13*2^n), A038550 (p*2^n, p odd prime), A065091 (odd primes), A061345 \ {1} (odd prime powers).

Select[Range[104], PrimePowerQ[#/2^IntegerExponent[#, 2]] &] (* Amiram Eldar, Jul 08 2020 *)

isA336101(n) = (1==omega(n>>valuation(n,2))); \\ Antti Karttunen, Jul 08 2020

A090994 Number of meaningful differential operations of the n-th order on the space R^9.

Original entry on oeis.org

9, 17, 32, 61, 116, 222, 424, 813, 1556, 2986, 5721, 10982, 21053, 40416, 77505, 148785, 285380, 547810, 1050876, 2017126, 3869845, 7427671, 14250855, 27351502, 52479500, 100719775, 193258375, 370895324, 711682501, 1365808847, 2620797529

Offset: 1

Branko Malesevic, Feb 29 2004

nonn

Also number of meaningful compositions of the n-th order of the differential operations and Gateaux directional derivative on the space R^8. - Branko Malesevic and Ivana Jovovic (ivana121(AT)EUnet.yu), Jun 21 2007
Also (starting 5,9,...) the number of zig-zag paths from top to bottom of a rectangle of width 10, whose color is that of the top right corner. [From Joseph Myers, Dec 23 2008]
Also, number of n-digit terms in A033075 (stated without proof in A033075). - Zak Seidov, Feb 02 2011

G. C. Greubel, Table of n, a(n) for n = 1..1000
B. Malesevic, Some combinatorial aspects of differential operation composition on the space R^n, Univ. Beograd, Publ. Elektrotehn. Fak., Ser. Mat. 9 (1998), 29-33.
Branko Malesevic, Some combinatorial aspects of differential operation compositions on space R^n, arXiv:0704.0750 [math.DG], 2007.
B. Malesevic and I. Jovovic, The Compositions of the Differential Operations and Gateaux Directional Derivative, arxiv:0706.0249 [math.CO], 2007.
Joseph Myers, BMO 2008--2009 Round 1 Problem 1---Generalisation
Index entries for linear recurrences with constant coefficients, signature (1, 4, -3, -3, 1).

Cf. A090989-A090995, A000079, A007283, A020701, A020714, A129638, A033075.

a:=[9,17,32,61,116];; for n in [6..40] do a[n]:=a[n-1]+4*a[n-2] - 3*a[n-3]-3*a[n-4]+a[n-5]; od; a; # G. C. Greubel, Feb 02 2019

m:=40; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(  x*(9+8*x-21*x^2-12*x^3+5*x^4)/(1-x-4*x^2+3*x^3+3*x^4-x^5) )); // G. C. Greubel, Feb 02 2019

NUM := proc(k :: integer) local i,j,n,Fun,Identity,v,A; n := 9; # <- DIMENSION Fun := (i,j)->piecewise(((j=i+1) or (i+j=n+1)),1,0); Identity := (i,j)->piecewise(i=j,1,0); v := matrix(1,n,1); A := piecewise(k>1,(matrix(n,n,Fun))^(k-1),k=1,matrix(n,n,Identity)); return(evalm(v&*A&*transpose(v))[1,1]); end:

LinearRecurrence[{1, 4, -3, -3, 1}, {9, 17, 32, 61, 116}, 31] (* Jean-François Alcover, Nov 20 2017 *)

my(x='x+O('x^40)); Vec(x*(9+8*x-21*x^2-12*x^3+5*x^4)/(1-x-4*x^2 +3*x^3+3*x^4-x^5)) \\ G. C. Greubel, Feb 02 2019

a=(x*(9+8*x-21*x^2-12*x^3+5*x^4)/(1-x-4*x^2+3*x^3+3*x^4-x^5)).series(x, 40).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Feb 02 2019

a(k+5) = a(k+4) + 4*a(k+3) - 3*a(k+2) - 3*a(k+1) + a(k).

G.f.: x*(9+8*x-21*x^2-12*x^3+5*x^4)/(1-x-4*x^2+3*x^3+3*x^4-x^5). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009; corrected by R. J. Mathar, Sep 16 2009

More terms from Joseph Myers, Dec 23 2008

A103694 Add 2 to each of the preceding digits, beginning with 0.

Original entry on oeis.org

0, 2, 4, 6, 8, 10, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 3, 3, 3, 2, 5, 5, 5, 4, 7, 7, 7, 6, 9, 9, 9, 8, 11, 11, 11, 10, 3, 3, 3, 3, 3, 3, 3, 2, 5, 5, 5, 5, 5, 5, 5, 4, 7, 7, 7, 7, 7, 7, 7, 6, 9, 9, 9, 9, 9, 9, 9, 8, 11, 11, 11, 11, 11, 11, 11, 10, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 5, 5, 5, 5, 5, 5

Offset: 0

Robert G. Wilson v, Feb 12 2005

A000225 is hidden here. The sequence shows increasing cycles of the ten digits 1,0,3,2,5,4,7,6,9,8 where the odd digits are repeated while the evens not. The second cycle is 11,10,3,3,3,2,5,5,5,4,7,7,7,6,9,9,9,8 (= three times the same odd digit); the third one shows seven same odd digit... Thus the number of repeating odd digits in the first cycles are: 1, 3, 7, 15, 31, 63, 127, ... which is the sequence A000225. - Alexandre Wajnberg, Feb 16 2005

A020714 is also hidden here: the total number of digits increasingly repeated of each of the cycles are: 5 (the first five digits), 10, 20, 40, 80, 160, 320, ... which is A020714. - Alexandre Wajnberg, Feb 16 2005

Robert Israel, Table of n, a(n) for n = 0..10000

Cf. A102654, A103693, A103695, A103696, A103697, A103698, A103699, A103700.

Cf. A000225, A020714.

V:= Vector([0]): B:= Vector([0]): m:= 1:
for n from 2 to 200 do
  V(n):= B[n-1] + 2;
  if V[n] >= 10 then
    B(m+1):= 1;
    B(m+2):= V[n] mod 10;
    m:= m+2;
  else
    B(m+1):= V[n];
    m:= m+1;
  fi
od:
convert(V,list); # Robert Israel, Oct 11 2016

Flatten[ NestList[ Function[x, Flatten[ IntegerDigits[x] + 2]], {0}, 22]]

From Robert Israel, Oct 11 2016: (Start)
For 6 <= m <= 10 and k >= 1, a(m*2^k-5) = 2*m-10.
For 5 <= m <= 9, k >= 1 and -4 <= j <= 2^k-6, a(m*2^k+j) = 2*m-7.
G.f.: (1-x)^(-1)*(2*(x+x^2+x^3+x^4)+3*x^5+Sum_{k>=1} ((-x-7)*x^(5*2^k-5)+Sum_{m=6..9} (-1+3*x)*x^(m*2^k-5))).
(End)

A110287 a(n) = 17*2^n.

Original entry on oeis.org

17, 34, 68, 136, 272, 544, 1088, 2176, 4352, 8704, 17408, 34816, 69632, 139264, 278528, 557056, 1114112, 2228224, 4456448, 8912896, 17825792, 35651584, 71303168, 142606336, 285212672, 570425344, 1140850688, 2281701376, 4563402752, 9126805504, 18253611008

Offset: 0

Alexandre Wajnberg, Sep 07 2005

The first differences are the sequence itself. Doubling the terms gives the same sequence (beginning one step further).

17 times powers of 2. - Omar E. Pol, Dec 17 2008

Vincenzo Librandi, Table of n, a(n) for n = 0..235
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (2).

Sequences of the form (2*m+1)*2^n: A000079 (m=0), A003945 (m=1), A020714 (m=2), A005009 (m=3), A005010 (m=4), A005015 (m=5), A005029 (m=6), A110286 (m=7), this sequence (m=8), A110288 (m=9), A175805 (m=10), A248646 (m=11), A164161 (m=12), A175806 (m=13), A257548 (m=15).

Cf. A007283.

[17*2^n: n in [0..40]]; // Vincenzo Librandi, Apr 28 2011

17*2^Range[0, 60] (* Vladimir Joseph Stephan Orlovsky, Jun 09 2011 *)
NestList[2#&,17,30] (* Harvey P. Dale, Jul 21 2014 *)

a(n)=17*2^n \\ Charles R Greathouse IV, Oct 07 2015

[17*2^n for n in range(51)] # G. C. Greubel, Jan 05 2023

G.f.: 17/(1-2*x). - Philippe Deléham, Nov 23 2008
a(n) = 17*A000079(n). - Omar E. Pol, Dec 17 2008
a(n) = 2*a(n-1) (with a(0)=17). - Vincenzo Librandi, Dec 26 2010
a(n) = A173786(n+4, n) for n>3. - Reinhard Zumkeller, Feb 28 2010
E.g.f.: 17*exp(2*x). - G. C. Greubel, Jan 05 2023

Edited by Omar E. Pol, Dec 16 2008

A146523 Binomial transform of A010685.

Original entry on oeis.org

1, 5, 10, 20, 40, 80, 160, 320, 640, 1280, 2560, 5120, 10240, 20480, 40960, 81920, 163840, 327680, 655360, 1310720, 2621440, 5242880, 10485760, 20971520, 41943040, 83886080, 167772160, 335544320, 671088640, 1342177280, 2684354560, 5368709120, 10737418240

Offset: 0

Philippe Deléham, Oct 30 2008

Linked to A029609 by a Catalan transform.

Hankel transform is (1, -15, 0, 0, 0, 0, 0, 0, 0, ...).

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

Cf. A010685, A020714, A029609, A084215, A109466.

CoefficientList[Series[(1+3x)/(1-2x), {x,0,50}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 21 2011 *)
Join[{1}, 5*2^(Range[40] -1)] (* G. C. Greubel, Nov 23 2021 *)

a(n)=if(n,5<<(n-1),1) \\ Charles R Greathouse IV, Jan 17 2012

[1]+[5*2^(n-1) for n in (1..50)] # G. C. Greubel, Nov 23 2021

a(n) = 5*2^(n-1) for n >= 1, a(0) = 1.
a(n) = Sum_{k=0..n} A109466(n,k)*A029609(k).
a(n) = A084215(n+1) = A020714(n-1), n > 0. - R. J. Mathar, Nov 02 2008
G.f.: (1 + 3*x)/(1 - 2*x). - Vladimir Joseph Stephan Orlovsky, Jun 21 2011
G.f.: G(0), where G(k)= 1 + 3*x/(1 -  2*x/(2*x + 3*x/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jul 03 2013
E.g.f.: (5*exp(2*x) - 3)/2. - Stefano Spezia, Feb 20 2023

A293157 Triangle read by rows: T(n,k) = number of linear chord diagrams with n chords such that every chord has length at least k (1 <= k <= n).

Original entry on oeis.org

1, 3, 1, 15, 5, 1, 105, 36, 10, 1, 945, 329, 99, 20, 1, 10395, 3655, 1146, 292, 40, 1, 135135, 47844, 15422, 4317, 876, 80, 1, 2027025, 721315, 237135, 69862, 16924, 2628, 160, 1, 34459425, 12310199, 4106680, 1251584, 332507, 67404, 7884, 320, 1, 654729075, 234615096, 79154927, 24728326, 6944594, 1627252, 269616, 23652, 640, 1

Offset: 1

N. J. A. Sloane, Oct 10 2017

There is a surprising change in notation in Sullivan (2016) between Definition 1 and Table 1.

The first 11 columns are given in the reference.

			Triangle begins:
      1;
      3,    1;
     15,    5,    1;
    105,   36,   10,    1;
    945,  329,   99,   20,    1;
  10395, 3655, 1146,  292,   40,    1;
  ...

Everett Sullivan, Linear chord diagrams with long chords, arXiv preprint arXiv:1611.02771 [math.CO], 2016.

Cf. A000806, A001147, A190823, A190824, A190825, A020714, A278990, A293156, A293881.

More terms from Alois P. Heinz, Oct 17 2017

A051633 a(n) = 5*2^n - 2.

Original entry on oeis.org

3, 8, 18, 38, 78, 158, 318, 638, 1278, 2558, 5118, 10238, 20478, 40958, 81918, 163838, 327678, 655358, 1310718, 2621438, 5242878, 10485758, 20971518, 41943038, 83886078, 167772158, 335544318, 671088638, 1342177278, 2684354558, 5368709118, 10737418238, 21474836478

Offset: 0

Asher Auel

			a(5) = 5*2^4 - 2 = 80 - 2 = 78.

Stefano Spezia, Table of n, a(n) for n = 0..3300
Index entries for linear recurrences with constant coefficients, signature (3,-2).

Cf. A000079, A020714, A118654.

Cf. A123208, A048487, A131051, A153894.

LinearRecurrence[{3, -2},{3, 8},30] (* Ray Chandler, Jul 18 2020 *)

a(n) = A118654(n, 5).
a(n) = A000079(n)*5 - 2 = A020714(n) - 2. - Omar E. Pol, Dec 23 2008
a(n) = 2*(a(n-1)+1) with a(0)=3. - Vincenzo Librandi, Aug 06 2010
a(n) = A123208(2*n+1) = A048487(n)+2 = A131051(n+2) = A153894(n)-1. - Philippe Deléham, Apr 15 2013
G.f.: ( 3-x ) / ( (2*x-1)*(x-1) ). - R. J. Mathar, Mar 23 2023
E.g.f.: exp(x)*(5*exp(x) - 2). - Stefano Spezia, Oct 03 2023

A051916 The Greek sequence: 2^a * 3^b * 5^c where a = 0,1,2,3,..., b,c in {0,1}, excluding the terms 1,2; that is: (a,b,c) != (0,0,0), (1,0,0).

Original entry on oeis.org

3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 256, 320, 384, 480, 512, 640, 768, 960, 1024, 1280, 1536, 1920, 2048, 2560, 3072, 3840, 4096, 5120, 6144, 7680, 8192, 10240, 12288, 15360, 16384, 20480

Offset: 1

Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), Dec 17 1999

From Reinhard Zumkeller, Mar 19 2010: (Start)
Union of A007283, A020707, A020714, and A110286.
Intersection of A051037 and A003401 apart from terms 1 and 2. (End)

George E. Martin, Geometric Constructions, New York: Springer, 1997, p. 140.

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,2).

Cf. A003401, A007283, A020707, A020714, A051037, A110286.

CoefficientList[Series[x(3x^7+2x^6+2x^5+2x^4+6x^3+5x^2+4x+3)/(1-2x^4),{x,0,60}],x] (* Harvey P. Dale, Dec 23 2012 *)

Vec(x*(3*x^7+2*x^6+2*x^5+2*x^4+6*x^3+5*x^2+4*x+3)/(1-2*x^4)+O(x^99)) \\ Charles R Greathouse IV, Oct 12 2012

def A051916(n): return n+2 if n<5 else (15,1,5,3)[m:=n&3]<<(n>>2)+(-2,2,0,1)[m] # Chai Wah Wu, Apr 02 2025

G.f.: x*(3*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 6*x^3 + 5*x^2 + 4*x + 3)/(1 - 2*x^4).
a(n+4) = 2*a(n) for n > 8. - Reinhard Zumkeller, Mar 19 2010
Sum_{n>=1} 1/a(n) = 17/10. - Amiram Eldar, Jan 18 2023

More terms from James Sellers, Dec 18 1999

Offset corrected by Reinhard Zumkeller, Mar 10 2010

A090990 Number of meaningful differential operations of the n-th order on the space R^5.

Original entry on oeis.org

5, 9, 16, 29, 52, 94, 169, 305, 549, 990, 1783, 3214, 5790, 10435, 18801, 33881, 61048, 110009, 198224, 357194, 643633, 1159797, 2089869, 3765830, 6785771, 12227562, 22033274, 39702627, 71541613, 128913593, 232294192, 418579765

Offset: 1

Branko Malesevic, Feb 29 2004

nonn

Also number of meaningful compositions of the n-th order of the differential operations and Gateaux directional derivative on the space R^4. - Branko Malesevic and Ivana Jovovic (ivana121(AT)EUnet.yu), Jun 21 2007

G. C. Greubel, Table of n, a(n) for n = 1..1000
Branko Malesevic, Some combinatorial aspects of differential operation composition on the space R^n, Univ. Beograd, Publ. Elektrotehn. Fak., Ser. Mat. 9 (1998), 29-33.
Branko Malesevic, Some combinatorial aspects of differential operation composition on the space R^n, arXiv:0704.0750 [math.DG], 2007.
Branko Malesevic and I. Jovovic, The Compositions of the Differential Operations and Gateaux Directional Derivative, arXiv:0706.0249 [math.CO], 2007.
Index entries for linear recurrences with constant coefficients, signature (1,2,-1).

Cf. A090989, A090991, A090992, A090993, A090994, A090995.

Cf. A000079, A007283, A020701, A020714, A129638.

a:=[5,9,16];; for n in [4..30] do a[n]:=a[n-1]+2*a[n-2]-a[n-3]; od; a; # G. C. Greubel, Feb 02 2019

m:=40; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(  x*(5+4*x-3*x^2)/(1-x-2*x^2+x^3) )); // G. C. Greubel, Feb 02 2019

NUM := proc(k :: integer) local i,j,n,Fun,Identity,v,A; n := 5; # <- DIMENSION Fun := (i,j)->piecewise(((j=i+1) or (i+j=n+1)),1,0); Identity := (i,j)->piecewise(i=j,1,0); v := matrix(1,n,1); A := piecewise(k>1,(matrix(n,n,Fun))^(k-1),k=1,matrix(n,n,Identity)); return(evalm(v&*A&*transpose(v))[1,1]); end:

LinearRecurrence[{1, 2, -1}, {5, 9, 16}, 32] (* Jean-François Alcover, Nov 22 2017 *)

my(x='x+O('x^40)); Vec(x*(5+4*x-3*x^2)/(1-x-2*x^2+x^3)) \\ G. C. Greubel, Feb 02 2019

a=(x*(5+4*x-3*x^2)/(1-x-2*x^2+x^3)).series(x, 40).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Feb 02 2019

a(n+3) = a(n+2) + 2*a(n+1) - a(n).

G.f.: x*(5+4*x-3*x^2)/(1-x-2*x^2+x^3). - Ralf Stephan, Aug 19 2004

More terms from Ralf Stephan, Aug 19 2004

More terms from Branko Malesevic and Ivana Jovovic (ivana121(AT)EUnet.yu), Jun 21 2007

A090992 Number of meaningful differential operations of the n-th order on the space R^7.

Original entry on oeis.org

7, 13, 24, 45, 84, 158, 296, 557, 1045, 1966, 3691, 6942, 13038, 24516, 46055, 86585, 162680, 305809, 574624, 1080106, 2029680, 3814941, 7169145, 13474502, 25322375, 47592650, 89441626, 168100324, 315917527, 593742597, 1115852904, 2097145317

Offset: 1

Branko Malesevic, Feb 29 2004

Also number of meaningful compositions of the n-th order of the differential operations and Gateaux directional derivative on the space R^6. - Branko Malesevic and Ivana Jovovic (ivana121(AT)EUnet.yu), Jun 21 2007

Also (starting 4,7,...) the number of zig-zag paths from top to bottom of a rectangle of width 8, whose color is that of the top right corner. - Joseph Myers, Dec 23 2008

G. C. Greubel, Table of n, a(n) for n = 1..1000
B. Malesevic, Some combinatorial aspects of differential operation composition on the space R^n, Univ. Beograd, Publ. Elektrotehn. Fak., Ser. Mat. 9 (1998), 29-33.
Branko Malesevic, Some combinatorial aspects of differential operation compositions on space R^n, arXiv:0704.0750 [math.DG], 2007.
B. Malesevic and I. Jovovic, The Compositions of the Differential Operations and Gateaux DirectionalDerivative, arXiv:0706.0249 [math.CO], 2007.
Joseph Myers, BMO 2008--2009 Round 1 Problem 1---Generalisation
2008/9 British Mathematical Olympiad Round 1: Thursday, 4 December 2008, Problem 1 [From _Joseph Myers_, Dec 23 2008]
Index entries for linear recurrences with constant coefficients, signature (1,3,-2,-1).

Cf. A090989-A090995.
Partial sums of pairwise sums of A065455.
Cf. A000079, A007283, A020701, A020714, A129638.

a:=[7,13,24,45];; for n in [5..40] do a[n]:=a[n-1]+3*a[n-2] - 2*a[n-3] - a[n-4]; od; a; # G. C. Greubel, Feb 02 2019

m:=40; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(  x*(7+6*x-10*x^2-4*x^3)/((1-x)*(1-3*x^2-x^3)) )); // G. C. Greubel, Feb 02 2019

NUM := proc(k :: integer) local i,j,n,Fun,Identity,v,A; n := 7; # <- DIMENSION Fun := (i,j)->piecewise(((j=i+1) or (i+j=n+1)),1,0); Identity := (i,j)->piecewise(i=j,1,0); v := matrix(1,n,1); A := piecewise(k>1,(matrix(n,n,Fun))^(k-1),k=1,matrix(n,n,Identity)); return(evalm(v&*A&*transpose(v))[1,1]); end:

LinearRecurrence[{1, 3, -2, -1}, {7, 13, 24, 45}, 32] (* Jean-François Alcover, Nov 25 2017 *)

my(x='x+O('x^40)); Vec(x*(7+6*x-10*x^2-4*x^3)/((1-x)*(1-3*x^2-x^3))) \\ G. C. Greubel, Feb 02 2019

a=(x*(7+6*x-10*x^2-4*x^3)/((1-x)*(1-3*x^2-x^3))).series(x, 40).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Feb 02 2019

a(n+4) = a(n+3) + 3*a(n+2) - 2*a(n+1) - a(n).

G.f.: x*(7+6*x-10*x^2-4*x^3)/((1-x)*(1-3*x^2-x^3)). - Colin Barker, Mar 08 2012

More terms from Branko Malesevic and Ivana Jovovic (ivana121(AT)EUnet.yu), Jun 21 2007

More terms from Joseph Myers, Dec 23 2008

cp's OEIS Frontend

A336101 Numbers divisible by exactly one odd prime.

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A090994 Number of meaningful differential operations of the n-th order on the space R^9.

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A103694 Add 2 to each of the preceding digits, beginning with 0.

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A110287 a(n) = 17*2^n.

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A146523 Binomial transform of A010685.

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A293157 Triangle read by rows: T(n,k) = number of linear chord diagrams with n chords such that every chord has length at least k (1 <= k <= n).

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A051633 a(n) = 5*2^n - 2.

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