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-2, -1, 1, 5, 13, 29, 61, 125, 253, 509, 1021, 2045, 4093, 8189, 16381, 32765, 65533, 131069, 262141, 524285, 1048573, 2097149, 4194301, 8388605, 16777213, 33554429, 67108861, 134217725, 268435453, 536870909, 1073741821, 2147483645
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| a(n+1) is the n-th number with exactly n 1's in binary representation. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 06 2003
Berstein and Onn: "For every m = 3k+1, the Graver complexity of the vertex-edge incidence matrix of the complete bipirtite graph K(3,m) satisfies g(m) >= 2^(k+2)-3." - Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 15 2007
Row sums of triangle A135857. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 01 2007
a(n) = A164874(n-1,n-2) for n>2. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 29 2009]
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 24 2010: (Start)
Starting (1, 5, 13,...) = eigensequence of a triangle with A016777:
(1, 4, 7, 10,...) as the left border and the rest 1's. (End)
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Aug 15 2010: (Start)
An elephant sequence, see A175655. For the central square just one A[5] vector, with decimal value 186, leads to this sequence (n>=2). For the corner squares this vector leads to the companion sequence A123203.
(End)
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..500
Yael Berstein, Shmuel Onn, The Graver Complexity of Integer Programming.
Index to sequences with linear recurrences with constant coefficients, signature (3,-2).
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FORMULA
| a(n)=2*a(n-1)+3
The sequence 1, 5, 13, ... has a(n)=4*2^n-3. These are the partial sums of A046055. - Paul Barry (pbarry(AT)wit.ie), Aug 25 2003
Row sums of triangle A130459 starting (1, 5, 13, 29, 61,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), May 26 2007
Row sums of triangle A131112 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 15 2007
Binomial transform of [1, 4, 4, 4,...] = (1, 5, 13, 29, 61...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 20 2007
a(n) = 2*StirlingS2(n,2) - 1, for n > 0. - Ross La Haye (rlahaye(AT)new.rr.com), Jul 05 2008
a(n) = A000079(n)-3. [From Omar E. Pol (info(AT)polprimos.com), Dec 21 2008]
G.f.: 1/(1-2*x)-3/(1-x). E.g.f.: e^(2*x)-3*e^x. [From Mohammad K. Azarian (azarian(AT)evansville.edu), Jan 14 2009]
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MATHEMATICA
| a=1; lst={a}; k=4; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 15 2008]
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PROG
| (Other) sage: [gaussian_binomial(n, 1, 2)-2 for n in xrange(0, 32)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 31 2009]
(MAGMA) [2^n-3: n in [0..40]]; // Vincenzo Librandi, May 09 2011
(PARI) a(n)= 2^n-3 \\ Charles R Greathouse IV, Dec 22 2011
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CROSSREFS
| Row sums of triangular array A027960. A column of A119725.
a(n) = A118654(n-3, 6), for n > 2.
Cf. A081118, A130459, A131112, A050414, A050415, A135857, A000079, A016777.
Sequence in context: A049252 A098315 A174986 * A025264 A139622 A204168
Adjacent sequences: A036560 A036561 A036562 * A036564 A036565 A036566
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KEYWORD
| sign,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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