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

Author

Giovanni Teofilatto, Oct 20 2010

Keywords

• easy
• nonn

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

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

Crossrefs

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

Programs

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;

Mathematica

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

Formula

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

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