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A001477 The nonnegative integers. 650
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

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

The number of partitions of 2n into exactly 2 parts. - Colin Barker, Mar 22 2015

The number of orbits of Aut(Z^7) as function of the infinity norm n of the representative lattice point of the orbit, when the cardinality of the orbit is equal to 8960 or 168.- Philippe A.J.G. Chevalier, Dec 29 2015

Partial sums give A000217. - Omar E. Pol, Jul 26 2018

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.

Hans Havermann, Table giving n and American English name for n, for 0 <= n <= 100999, without spaces or hyphens

Hans Havermann, American English number names to one million, without spaces or hyphens

Tanya Khovanova, Recursive Sequences

Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.

László Németh, The trinomial transform triangle, J. Int. Seqs., Vol. 21 (2018), Article 18.7.3. Also arXiv:1807.07109 [math.NT], 2018.

Eric Weisstein's World of Mathematics, Natural Number

Eric Weisstein's World of Mathematics, Nonnegative Integer

Index entries for "core" sequences

Index entries for sequences that are permutations of the natural numbers

Index entries for 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

a(0)=0, a(n>0) = 2z(-1)^[( |z|/z + 3 )/2] + ( |z|/z - 1 )/2 for z=A130472(n>0); a 1_to_1 correspondence between integers and naturals. - Adriano Caroli, Mar 29 2015

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.

Number of orbits of Aut(Z^7) as function of the infinity norm A000579, A154286, A102860, A002412, A045943, A115067, A008586, A008585, A005843, A000217.

Sequence in context: A303502 A000027 * A087156 A254109 A317945 A292579

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 December 14 14:37 EST 2018. Contains 318098 sequences. (Running on oeis4.)