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A181440
a(1) = 2; for n > 1, a(n) = A000217(n)-(sum of previous terms).
3
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
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
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