A005015 -id:A005015 - cp's OEIS frontend

A005009 a(n) = 7*2^n.

7, 14, 28, 56, 112, 224, 448, 896, 1792, 3584, 7168, 14336, 28672, 57344, 114688, 229376, 458752, 917504, 1835008, 3670016, 7340032, 14680064, 29360128, 58720256, 117440512, 234881024, 469762048, 939524096, 1879048192, 3758096384

Offset: 0

N. J. A. Sloane

The first differences are the sequence itself. - Alexandre Wajnberg & Eric Angelini, Sep 07 2005

Vincenzo Librandi, Table of n, a(n) for n = 0..3000
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), A007283 (m=1), A020714 (m=2), this sequence (m=3), A005010 (m=4), A005015 (m=5), A005029 (m=6), A110286 (m=7), A110287 (m=8), A110288 (m=9), A175805 (m=10), A248646 (m=11), A164161 (m=12), A175806 (m=13), A257548 (m=15).
Row sums of (6, 1)-Pascal triangle A093563 and of (1, 6)-Pascal triangle A096956, n>=1.
Cf. A000120, A014311, A118416, A173787, A212191.

a005009 = (* 7) . (2 ^) -- Reinhard Zumkeller, May 03 2012

[7*2^n:n in [0..50]]; // Vincenzo Librandi, Sep 20 2011

7*2^Range[0,50] (* Vladimir Joseph Stephan Orlovsky, Mar 14 2011 *)
NestList[2#&,7,30] (* Harvey P. Dale, Aug 10 2024 *)

a(n)=7<Charles R Greathouse IV, Dec 22 2011

[7*2^n for n in range(51)] # G. C. Greubel, Jan 05 2023

G.f.: 7/(1-2*x).
a(n) = A118416(n+1,4) for n > 3. - Reinhard Zumkeller, Apr 27 2006
a(n) = 2*a(n-1), for n > 0, with a(0)=7 . - Philippe Deléham, Nov 23 2008
a(n) = 7 * A000079(n). - Omar E. Pol, Dec 16 2008
a(n) = A173787(n+3,n). - Reinhard Zumkeller, Feb 28 2010
Intersection of A014311 and A212191: all terms and their squares are the sum of exactly three distinct powers of 2, A000120(a(n)) = A000120(a(n)^2) = 3. - Reinhard Zumkeller, May 03 2012
G.f.: 2/x/G(0) - 1/x + 9, where G(k)= 1 + 1/(1 - x*(7*k+2)/(x*(7*k+9) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 03 2013
E.g.f.: 7*exp(2*x). - Stefano Spezia, May 15 2021

A093645 (10,1) Pascal triangle.

Original entry on oeis.org

1, 10, 1, 10, 11, 1, 10, 21, 12, 1, 10, 31, 33, 13, 1, 10, 41, 64, 46, 14, 1, 10, 51, 105, 110, 60, 15, 1, 10, 61, 156, 215, 170, 75, 16, 1, 10, 71, 217, 371, 385, 245, 91, 17, 1, 10, 81, 288, 588, 756, 630, 336, 108, 18, 1, 10, 91, 369, 876, 1344, 1386, 966, 444, 126, 19, 1

Offset: 0

Wolfdieter Lang, Apr 22 2004

The array F(10;n,m) gives in the columns m >= 1 the figurate numbers based on A017281, including the 12-gonal numbers A051624 (see the W. Lang link).
This is the tenth member, d=10, in the family of triangles of figurate numbers, called (d,1) Pascal triangles: A007318 (Pascal), A029653, A093560-5 and A093644 for d=1..9.
This is an example of a Riordan triangle (see A093560 for a comment and A053121 for a comment and the 1991 Shapiro et al. reference on the Riordan group). Therefore the o.g.f. for the row polynomials p(n,x) := Sum_{m=0..n} a(n,m)*x^m is G(z,x) = (1+9*z)/(1-(1+x)*z).
The SW-NE diagonals give A022100(n-1) = Sum_{k=0..ceiling((n-1)/2)} a(n-1-k, k), n >= 1, with n=0 value 9. Observation by Paul Barry, Apr 29 2004. Proof via recursion relations and comparison of inputs.

			Triangle begins
   1;
  10,  1;
  10, 11,  1;
  10, 21, 12,  1;
  ...

Kurt Hawlitschek, Johann Faulhaber 1580-1635, Veroeffentlichung der Stadtbibliothek Ulm, Band 18, Ulm, Germany, 1995, Ch. 2.1.4. Figurierte Zahlen.
Ivo Schneider: Johannes Faulhaber 1580-1635, Birkhäuser, Basel, Boston, Berlin, 1993, ch. 5, pp. 109-122.

Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened
W. Lang, First 10 rows and array of figurate numbers .

Row sums: 1 for n=0 and A005015(n-1), n >= 1, alternating row sums are 1 for n=0, 9 for n=2 and 0 otherwise.

The column sequences give for m=1..9: A017281, A051624 (12-gonal), A007587, A051799, A051880, A050406, A052254, A056125, A093646.

a093645 n k = a093645_tabl !! n !! k
a093645_row n = a093645_tabl !! n
a093645_tabl = [1] : iterate
               (\row -> zipWith (+) ([0] ++ row) (row ++ [0])) [10, 1]
-- Reinhard Zumkeller, Aug 31 2014

t[0, 0] = 1; t[n_, k_] := Binomial[n, k] + 9*Binomial[n-1, k]; Table[t[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jul 05 2013, after Philippe Deléham *)

a(n, m) = F(10;n-m, m) for 0 <= m <= n, else 0, with F(10;0, 0)=1, F(10;n, 0)=10 if n >= 1 and F(10;n, m):=(10*n+m)*binomial(n+m-1, m-1)/m if m >= 1.
Recursion: a(n, m)=0 if m > n, a(0, 0)=1; a(n, 0)=10 if n >= 1; a(n, m) = a(n-1, m) + a(n-1, m-1).
G.f. column m (without leading zeros): (1+9*x)/(1-x)^(m+1), m >= 0.
T(n, k) = C(n, k) + 9*C(n-1, k). - Philippe Deléham, Aug 28 2005
exp(x) * e.g.f. for row n = e.g.f. for diagonal n. For example, for n = 3 we have exp(x)*(10 + 21*x + 12*x^2/2! + x^3/3!) = 10 + 31*x + 64*x^2/2! + 110*x^3/3! + 170*x^4/4! + .... The same property holds more generally for Riordan arrays of the form ( f(x), x/(1 - x) ). - Peter Bala, Dec 22 2014

A110286 a(n) = 15*2^n.

Original entry on oeis.org

15, 30, 60, 120, 240, 480, 960, 1920, 3840, 7680, 15360, 30720, 61440, 122880, 245760, 491520, 983040, 1966080, 3932160, 7864320, 15728640, 31457280, 62914560, 125829120, 251658240, 503316480, 1006632960, 2013265920, 4026531840, 8053063680, 16106127360

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).

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).

Cf. A007283, A020714, A005009, A005010, A005015, A005029.

Cf. A000079, A051916, A173787.

[15*2^n: n in [0..40]]; // Vincenzo Librandi, Apr 28 2011

15*2^Range[0, 60] (* Vladimir Joseph Stephan Orlovsky, Jun 09 2011 *)
NestList[2#&,15,30] (* Harvey P. Dale, Oct 19 2014 *)

a(n)=15<Charles R Greathouse IV, Oct 07 2015

G.f.: 15/(1-2x). - Philippe Deléham, Nov 23 2008
a(n) = A000079(n)*15 = A007283(n)*5 = A020714(n)*3. - Omar E. Pol, Dec 17 2008
a(n) = A173787(n+4,n). - Reinhard Zumkeller, Feb 28 2010
Subsequence of A051916. - Reinhard Zumkeller, Mar 20 2010
a(n) = 2*a(n-1) (with a(0)=15). - Vincenzo Librandi, Dec 26 2010
E.g.f.: 15*exp(2*x). - Stefano Spezia, May 15 2021

Edited by Omar E. Pol, Dec 16 2008

A030067 The "Semi-Fibonacci sequence": a(1) = 1; a(n) = a(n/2) (n even); a(n) = a(n-1) + a(n-2) (n odd).

Original entry on oeis.org

1, 1, 2, 1, 3, 2, 5, 1, 6, 3, 9, 2, 11, 5, 16, 1, 17, 6, 23, 3, 26, 9, 35, 2, 37, 11, 48, 5, 53, 16, 69, 1, 70, 17, 87, 6, 93, 23, 116, 3, 119, 26, 145, 9, 154, 35, 189, 2, 191, 37, 228, 11, 239, 48, 287, 5, 292, 53, 345, 16, 361, 69, 430, 1, 431, 70, 501, 17, 518, 87, 605, 6, 611, 93

Offset: 1

David W. Wilson

This is the "semi-Fibonacci sequence". The distinct numbers that appear are called "semi-Fibonacci numbers", and are given in A030068.
a(2n+1) >= a(2n-1) + 1 is monotonically increasing. a(2n)/n can be arbitrarily small, as a(2^n) = 1. There are probably an infinite number of primes in the sequence. - Jonathan Vos Post, Mar 28 2006
From Robert G. Wilson v, Jan 17 2014: (Start)
Positions where k occurs:
   k: sequence
   -:-----------------------------
   1: A000079;
   2: 3*A000079 = A007283;
   3: 5*A000079 = A020714;
   4: none in the first 10^6 terms;
   5: 7*A000079 = A005009;
   6: 9*A000079 = A005010;
   7: none in the first 10^6 terms;
   8: none in the first 10^6 terms;
   9: 11*A000079 = A005015;
  10: none in the first 10^6 terms;
  11: 13*A000079 = A005029;
  12: none in the first 10^6 terms;
(End)
Any integer N which occurs in this sequence first occurs as an odd-indexed term a(2k-1) = A030068(k-1), and thereafter at indices (2k-1)*2^j, j=1,2,3,... (Both of these statements follow immediately from the definition of even-indexed terms.) No N can occur a second time as an odd-indexed term: This follows from the definition of these terms, a(2n+1) = a(2n) + a(2n-1) = a(2n-1) + a(n), which shows that the subsequence of odd-indexed terms (A030068) is strictly increasing, and therefore equal to the range (or: set) of the semi-Fibonacci numbers. - M. F. Hasler, Mar 24 2017
The lines in the logarithmic scatterplot of the sequence corresponds to sets of indices with the same 2-adic valuation. - Rémy Sigrist, Nov 27 2017
Define the partition subsum polynomial of an integer partition m of n where m = (m_1, m_2, ...m_k) by ps(m,x) = Product_{i=1..k} (1+x^m_i). Expanding ps(m,x) gives 1+a_1 x+a_2 x^2+...+a_n x^n, where a_j is the number of ways to form the subsum j from the parts of m. Then the number of partitions m of n for which ps(m,x) has no repeated root is a(n). - George Beck, Nov 07 2018

			a(1) = 1 by definition.
a(2) = a(1) = 1.
a(3) = 1 + 1 = 2.
a(4) = a(2) = 1.
a(5) = 2 + 1 = 3.
a(6) = a(3) = 2.
a(7) = 3 + 2 = 5.
a(8) = a(4) = 1.
a(9) = 5 + 1 = 6.
a(10) = a(5) = 3.

T. D. Noe, Table of n, a(n) for n = 1..10000
Abdulaziz M. Alanazi, Augustine O. Munagi and Darlison Nyirenda, Power Partitions and Semi-m-Fibonacci Partitions, arXiv:1910.09482 [math.CO], 2019.
George E. Andrews, Binary and Semi-Fibonacci Partitions, Journal of Ramanujan Society of Mathematics and Mathematics Sciences, honoring A.K. Agarwal's 70th birthday, 7:1(2019), 01-06.
Cristina Ballantine and George Beck, Partitions enumerated by self-similar sequences, arXiv:2303.11493 [math.CO], 2023.
George Beck, Semi-Fibonacci Partitions
Rémy Sigrist, Colored logarithmic scatterplot of the first 10000 terms (where the color is function of the 2-adic valuation of n)

Cf. A000045, A030068, A074364, A129092, A129100.

See A109671 for a variant.

import Data.List (transpose)
a030067 n = a030067_list !! (n-1)
a030067_list = concat $ transpose [scanl (+) 1 a030067_list, a030067_list]
-- Reinhard Zumkeller, Jul 21 2013, Jul 07 2013

f:=proc(n) option remember; if n=1 then RETURN(1) elif n mod 2 = 0 then RETURN(f(n/2)) else RETURN(f(n-1)+f(n-2)); fi; end;

semiFibo[1] = 1; semiFibo[n_?EvenQ] := semiFibo[n] = semiFibo[n/2]; semiFibo[n_?OddQ] := semiFibo[n] = semiFibo[n - 1] + semiFibo[n - 2]; Table[semiFibo[n], {n, 80}] (* Jean-François Alcover, Aug 19 2013 *)

a(n) = if(n==1, 1, if(n%2 == 0, a(n/2), a(n-1) + a(n-2)));
vector(100, n, a(n)) \\ Altug Alkan, Oct 12 2015

a=[1]; [a.append(a[-2]+a[-1] if n%2 else a[n//2-1]) for n in range(2, 75)]
print(a) # Michael S. Branicky, Jul 07 2022

Theorem: a(2n+1) - a(2n-1) = a(n). Proof: a(2n+1) - a(2n-1) = a(2n) + a(2n-1) - a(2n-2) - a(2n-3) = a(n) - a(n-1) + a(n-1) (induction) = a(n). - N. J. A. Sloane, May 02 2010
a(2^n - 1) = A129092(n) for n >= 1, where A129092 forms the row sums and column 0 of triangle A129100, which is defined by the nice property that column 0 of matrix power A129100^(2^k) = column k of A129100 for k > 0. - Paul D. Hanna, Dec 03 2008
G.f. g(x) satisfies (1-x^2) g(x) = (1+x-x^2) g(x^2) + x. - Robert Israel, Mar 23 2017

A091629 Product of digits associated with A091628(n). Essentially the same as A007283.

Original entry on oeis.org

6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196608, 393216, 786432, 1572864, 3145728, 6291456, 12582912, 25165824, 50331648, 100663296, 201326592, 402653184, 805306368, 1610612736, 3221225472

Offset: 1

Enoch Haga, Jan 24 2004

Sequence arising in Farideh Firoozbakht's solution to Prime Puzzle 251 - 23 is the only pointer prime (A089823) not containing digit "1".

The monotonic increasing value of successive product of digits strongly suggests that in successive n the digit 1 must be present.

G. C. Greubel, Table of n, a(n) for n = 1..1000
Tanya Khovanova, Recursive Sequences
Carlos Rivera, Puzzle 251, Pointer primes, The Prime Puzzles and Problems Connection.
Index entries for linear recurrences with constant coefficients, signature (2).

Sequences of the form (2*m+1)*2^n: A000079 (m=0), A007283 (m=1), A020714 (m=2), A005009 (m=3), A005010 (m=4), A005015 (m=5), A005029 (m=6), A110286 (m=7), A110287 (m=8), A110288 (m=9), A175805 (m=10), A248646 (m=11), A164161 (m=12), A175806 (m=13), A257548 (m=15).
Cf. A089823, A091628, A091630, A091631, A091632.
Similar to A003945, A042950, A058764, A087009, A081808.

[3*2^n : n in [1..40]]; // Wesley Ivan Hurt, Jul 17 2020

3*2^Range[1, 60] (* Vladimir Joseph Stephan Orlovsky, Jun 09 2011 *)

[3*2^n for n in range(1,51)] # G. C. Greubel, Jan 05 2023

a(n) = 3 * 2^n = product of digits of A091628(n).
From Philippe Deléham, Nov 23 2008: (Start)
a(n) = 6*2^(n-1).
a(n) = 2*a(n-1), with a(1) = 6.
G.f.: 6*x/(1-2*x). (End)
E.g.f.: 3*(exp(2*x) - 1). - G. C. Greubel, Jan 05 2023

Edited and extended by Ray Chandler, Feb 07 2004

A336101 Numbers divisible by exactly one odd prime.

Original entry on oeis.org

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

A002089 a(n) = 11*4^n.

Original entry on oeis.org

11, 44, 176, 704, 2816, 11264, 45056, 180224, 720896, 2883584, 11534336, 46137344, 184549376, 738197504, 2952790016, 11811160064, 47244640256, 188978561024, 755914244096, 3023656976384, 12094627905536, 48378511622144, 193514046488576, 774056185954304, 3096224743817216

Offset: 0

N. J. A. Sloane

Subsequence of A000069, the odious numbers. - Reinhard Zumkeller, Aug 26 2007

Vincenzo Librandi, Table of n, a(n) for n = 0..500
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (4).

Bisection of A005015. Half the first differences of A072261.

[11*4^n: n in [0..30]]; // Vincenzo Librandi, May 31 2011

A002089:=n->11*4^n; seq(A002089(n), n=0..100); # Wesley Ivan Hurt, Nov 12 2013

11*4^Range[0, 100] (* Vladimir Joseph Stephan Orlovsky, Jun 09 2011 *)
NestList[4#&,11,30] (* Harvey P. Dale, Jun 19 2014 *)

a(n)=11*4^n \\ Charles R Greathouse IV, Apr 18 2012

From Philippe Deléham, Nov 23 2008: (Start)
a(n) = 4*a(n-1); a(0)=11.
G.f.: 11/(1-4*x). (End)
a(n) = 11*A000302(n). - Michel Marcus, Nov 13 2013
From Elmo R. Oliveira, Apr 02 2025: (Start)
E.g.f.: 11*exp(4*x).
a(n) = A005015(2*n). (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

A086225 a(n) = 11*2^n - 1.

Original entry on oeis.org

10, 21, 43, 87, 175, 351, 703, 1407, 2815, 5631, 11263, 22527, 45055, 90111, 180223, 360447, 720895, 1441791, 2883583, 5767167, 11534335, 23068671, 46137343, 92274687, 184549375, 369098751, 738197503, 1476395007, 2952790015

Offset: 0

Marco Matosic, Jul 29 2003

(a(n-1))^2 + a(n) is a square. - Vincenzo Librandi, Aug 08 2010

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Gennady Eremin, Partitioning the set of natural numbers into Mersenne trees and into arithmetic progressions; Natural Matrix and Linnik's constant, arXiv:2405.16143 [math.CO], 2024. See pp. 3-4.
Index entries for linear recurrences with constant coefficients, signature (3,-2).

Cf. A000079, A005015.

NestList[2#+1&,10,30] (* or *) LinearRecurrence[{3,-2},{10,21},30] (* Harvey P. Dale, Nov 25 2013 *)

a(n) = 11*2^n - 1 \\ Michel Marcus, Jul 15 2013

a(n) = 2*a(n-1) + 1.
G.f.: (10 - 9*x)/((2*x - 1)*(x - 1)). - R. J. Mathar, Oct 22 2011
E.g.f.: exp(x)*(11*exp(x) - 1). - Stefano Spezia, May 05 2025

A110288 a(n) = 19*2^n.

Original entry on oeis.org

19, 38, 76, 152, 304, 608, 1216, 2432, 4864, 9728, 19456, 38912, 77824, 155648, 311296, 622592, 1245184, 2490368, 4980736, 9961472, 19922944, 39845888, 79691776, 159383552, 318767104, 637534208, 1275068416, 2550136832, 5100273664, 10200547328, 20401094656

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).

19 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), A007283 (m=1), A020714 (m=2), A005009 (m=3), A005010 (m=4), A005015 (m=5), A005029 (m=6), A110286 (m=7), A110287 (m=8), this sequence (m=9), A175805 (m=10), A248646 (m=11), A164161 (m=12), A175806 (m=13), A257548 (m=15).

[19*2^n: n in [0..40]]; // Vincenzo Librandi, Apr 28 2011

19*2^Range[0, 60] (* Vladimir Joseph Stephan Orlovsky, Jun 09 2011 *)
NestList[2#&,19,30] (* Harvey P. Dale, May 11 2018 *)

[19*2^n for n in range(41)] # G. C. Greubel, Jan 04 2023

G.f.: 19/(1-2*x). - Philippe Deléham, Nov 23 2008
a(n) = A000079(n)*19. - Omar E. Pol, Dec 17 2008
E.g.f.: 19*exp(2*x). - G. C. Greubel, Jan 04 2023

Edited by Omar E. Pol, Dec 16 2008

cp's OEIS Frontend

A005009 a(n) = 7*2^n.

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A093645 (10,1) Pascal triangle.

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Haskell

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Formula

A110286 a(n) = 15*2^n.

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Magma

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A030067 The "Semi-Fibonacci sequence": a(1) = 1; a(n) = a(n/2) (n even); a(n) = a(n-1) + a(n-2) (n odd).

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Haskell

Maple

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A091629 Product of digits associated with A091628(n). Essentially the same as A007283.

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Magma

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SageMath

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A336101 Numbers divisible by exactly one odd prime.

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A002089 a(n) = 11*4^n.