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A001477
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The nonnegative integers.
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366
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77
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OFFSET
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0,3
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COMMENTS
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Although this is a list, and lists normally have offset 1, it seems better to make an exception in this case. - N. J. A. Sloane, Mar 13 2010
The subsequence 0,1,2,3,4 gives the known values of n such that 2^(2^n)+1 is a prime (see A019434, the Fermat primes). - N. J. A. Sloane, Jun 16 2010.
a(n) = A007966(n)*A007967(n). [Reinhard Zumkeller, Jun 18 2011]
Besides the first term, this sequence is the denominator in the Maclaurin series of ln 2, which is 1 - 1/2 + 1/3 - 1/4 +.... - Mohammad K. Azarian, Oct 15 2011
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REFERENCES
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Paul Barry, A Catalan Transform and Related Transformations on Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5.
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 0..500000
Tanya Khovanova, Recursive Sequences
Eric Weisstein's World of Mathematics, Natural Number
Eric Weisstein's World of Mathematics, Nonnegative Integer
Robert G. Wilson v, American English names for the numbers from 0 to 100999 without spaces or hyphens.
Index entries for "core" sequences
Index entries for sequences that are permutations of the natural numbers
Index entries for sequences related to linear recurrences with constant coefficients, signature (2,-1).
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FORMULA
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a(n)=n; a(0) = 0, a(n) = a(n-1)+1; G.f.: x/(1-x)^2.
Multiplicative with a(p^e) = p^e. - David W. Wilson, Aug 01, 2001.
When seen as array: T(k, n) = n + (k+n)*(k+n+1)/2. Main diagonal is 2n(n+1) (A046092), antidiagonal sums are n(n+1)(n+2)/2 (A027480). - Ralf Stephan, Oct 17 2004
Dirichlet generating function: zeta(s-1). - Franklin T. Adams-Watters, Sep 11 2005.
E.g.f. x*e^x. - Franklin T. Adams-Watters, Sep 11 2005.
a(0)=0, a(1)=1, a(n)=2*a(n-1)-a(n-2). - Jaume Oliver Lafont, May 07 2008
Contribution from Eric Desbiaux, Oct 28 2008: Alternating partial sums give A001057 = A000217 - 2*(A008794)
a(n) = 2*A080425(n)+3*A008611(n-3), n>1. - Eric Desbiaux, Nov 15 2009
a(n)=Sum_k>=0 {A030308(n,k)*2^k}. - From Philippe Deléham, Oct 20 2011.
a(n) = 2*A028242(n-1) + (-1)^n*A000034(n-1). - R. J. Mathar, Jul 20 2012
E.g.f.: - G(0) where G(k) = 1 - (k+1)/(1 - x/(x - (k+1)^2/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Dec 06 2012
a(n+1) = det(C(i+1,j), 1 <= i,j <= n), where C(n,k) are binomial coefficients. [Mircea Merca, Apr 06 2013]
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EXAMPLE
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Triangular view:
0 ;
1 2 ;
3 4 5 ;
6 7 8 9 ;
10 11 12 13 14 ;
15 16 17 18 19 20 ;
21 22 23 24 25 26 27 ;
28 29 30 31 32 33 34 35 ;
36 37 38 39 40 41 42 43 44 ;
45 46 47 48 49 50 51 52 53 54 ;
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MAPLE
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[ seq(n, n=0..100) ];
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MATHEMATICA
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Table[n, {n, 0, 100}] - Stefan Steinerberger, Apr 08 2006
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PROG
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(MAGMA) [ n : n in [0..100]];
(PARI) A001477(n)=n /* first term is a(0) */
(Haskell)
a001477 = id
a001477_list = [0..] -- Reinhard Zumkeller, May 07 2012
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CROSSREFS
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Cf. A000027 (n>=1).
Partial sums of A057427. - Jeremy Gardiner, Sep 08 2002
Cf. A038608 (alternating signs), A001787 (binomial transform).
Cf. A055112.
Sequence in context: A131738 A000027 * A087156 A033619 A130734 A090108
Adjacent sequences: A001474 A001475 A001476 * A001478 A001479 A001480
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KEYWORD
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core,nonn,easy,mult,tabl
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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