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 A001477 The nonnegative integers. 698
 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 First differences are A000012 (the "all 1's" sequence). - M. F. Hasler, May 30 2020 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 [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 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 2*n*(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) = 2*z(-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). Cf. A000012 (first differences). 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. When written as an array, the rows/columns are A000217, A000124, A152948, A152950, A145018, A167499, A166136, A167487... and A000096, A034856, A055998, A046691, A052905, A055999... (with appropriate offsets); cf. analogous lists for A000027 in A185787. Cf. A000290. Sequence in context: A199969 A303502 A000027 * A087156 A254109 A317945 Adjacent sequences:  A001474 A001475 A001476 * A001478 A001479 A001480 KEYWORD core,nonn,easy,mult,tabl AUTHOR STATUS approved

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Last modified October 29 03:28 EDT 2020. Contains 338065 sequences. (Running on oeis4.)