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A001477 The nonnegative integers. 435
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

Also: The identity map, defined on the set of nonnegative integers. The restriction to the positive integers yields the sequence A000027. - M. F. Hasler, Nov 20 2013

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 0..500000

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

Tanya Khovanova, Recursive Sequences

Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081, 2014

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

Alternating partial sums give A001057 = A000217 - 2*(A008794). - Eric Desbiaux, Oct 28 2008

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}. - Philippe Deléham, Oct 20 2011

a(n) = 2*A028242(n-1) + (-1)^n*A000034(n-1). - R. J. Mathar, Jul 20 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

a(n-1) = floor(n/e^(1/n)) for n > 0. - Richard R. Forberg, Jun 22 2013

a(n) = A000027(n) for all n>0.

a(n) = floor(cot(1/(n+1))).  - Clark Kimberling, Oct 08 2014

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 *)

LinearRecurrence[{2, -1}, {0, 1}, 77] (* Robert G. Wilson v, May 23 2013 *)

CoefficientList[ Series[x/(x - 1)^2, {x, 0, 76}], x] (* Robert G. Wilson v, May 23 2013 *)

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.

Cf. Boustrophedon transforms: A231179, A000737.

Cf. A245422.

Sequence in context: A131738 A000027 * A087156 A033619 A130734 A244581

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 November 23 04:28 EST 2014. Contains 249839 sequences.