A181440 a(1) = 2; for n > 1, a(n) = A000217(n)-(sum of previous terms).

2, 1, 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

Offset

1,1

Comments

2 followed by A065475, or A000027 with first and second term interchanged.

It can be observed that this sequence is an "autosequence", that is a sequence which is identical to its inverse binomial transform, except for signs. More precisely, it is an autosequence "of the second kind", since the main diagonal of the successive differences array is twice the first upper diagonal. - Jean-François Alcover, Jul 25 2016

Links

Table of n, a(n) for n=1..72.

OEIS Wiki, Autosequence

Wikipedia, Autosuite de nombres (in French).

Index entries for linear recurrences with constant coefficients, signature (2, -1).

Formula

G.f.: x*(2-x)*(1-x+x^2) / (1-x)^2. - Joerg Arndt, Jul 25 2016

Mathematica

a = {2}; Do[AppendTo[a, ((n^2 + n)/2) - Total@ a], {n, 2, 72}]; a (* Michael De Vlieger, Jul 25 2016 *)

Prog

(Magma) S:=[2]; s:=2; for n in [2..80] do a:=Binomial(n+1, 2)-s; Append(~S, a); s+:=a; end for; S;

Crossrefs

Cf. A000027 (natural numbers), A000217 (triangular numbers), A065475 (natural numbers excluding 2).

Sequence in context: A360585 A175499 A340684 * A035043 A288118 A155963

Adjacent sequences: A181437 A181438 A181439 * A181441 A181442 A181443

Keyword

easy,nonn

Author

Giovanni Teofilatto, Oct 20 2010

Extensions

Edited by Klaus Brockhaus, Oct 26 2010

A171950 and A181440 are two different edited versions of a sequence submitted by Giovanni Teofilatto. - N. J. A. Sloane, Oct 29 2010

Status

approved