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A001477 The nonnegative integers. 366
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

REFERENCES

Paul Barry, A Catalan Transform and Related Transformations on Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5.

LINKS

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).

FORMULA

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]

EXAMPLE

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 ;

MAPLE

[ seq(n, n=0..100) ];

MATHEMATICA

Table[n, {n, 0, 100}] - Stefan Steinerberger, Apr 08 2006

PROG

(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

CROSSREFS

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

KEYWORD

core,nonn,easy,mult,tabl

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified May 22 11:54 EDT 2013. Contains 225529 sequences.