0,2

Numbers n such that concatenation of first n natural numbers is not divisible by 3. E.g. 16 is in the sequence because we have 123456789101111213141516 = 1 (mod 3).

Ignoring the first term, this sequence represents the number of bonds in a hydrocarbon: a(#of carbon atoms)=number of bonds. - Nathan Savir (thoobik(AT)yahoo.com), Jul 03 2003

n such that sum(k=0,n,binomial(n+k,n-k) mod 2) is even (cf. A007306) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 09 2004

Number of vertices of squares sharing a common vertex. - Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Nov 11 2005

Hilbert series for twisted cubic curve. - Paul Barry (pbarry(AT)wit.ie), Aug 11 2006

If Y is a 3-subset of an n-set X then, for n>=3, a(n-3) is the number of 3-subsets of X having at least two elements in common with Y. - Milan R. Janjic (agnus(AT)blic.net), Nov 23 2007

Konrad Knopp, Theory and Application of Infinite Series, Dover, p. 269.

W. Decker, C. Lossen, Computing in Algebraic Geometry, Springer, 2006, p. 22

L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 16.

Tanya Khovanova, Recursive Sequences

L. Euler, Observatio de summis divisorum p. 9.

L. Euler, An observation on the sums of divisors p. 9.

Konrad Knopp, Theorie und Anwendung der unendlichen Reihen, Berlin, J. Springer, 1922. (Original German edition of "Theory and Application of Infinite Series")

T. Mansour, Permutations avoiding a set of patterns T \subseteq S_3 and a pattern \tau \in S_4

G.f.: (1+2*x)/(1-x)^2. a(n)=3+a(n-1).

sum(n=1, inf, (-1)^n/a(n))=1/3(Pi/sqrt(3)+ln(2)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 05 2002

(1 + 4x + 7x^2 + 10x^3...) = (1 + 2x + 3x^2...) / (1 - 2x + 4x^2 - 8x^3...) - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 03 2003

E.g.f. : exp(x)(1+3x) - Paul Barry (pbarry(AT)wit.ie), Jul 23 2003

1 - 1/4 + 1/7 - 1/10... = (1/3)*(Pi/(sqrt(3) + ln 2). [Jolley] - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 16 2006

Row sums of triangle A131033: (1; 3,1; 4,2,1; 5,2,2,1;...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 10 2007

a[0]:=0:a[1]:=1:for n from 2 to 100 do a[n]:=a[n-1]+3 od: seq(a[n], n=1..63); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 16 2008

(MAGMA) [ 3*n+1 : n in [1..10] ]; - from Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006

A016789(n)=1+A016777(n).

Cf. A058183.

First differences of A000326.

Cf. A131033.

Sequence in context: A026314 A070300 A112335 this_sequence A004084 A121381 A046956

Adjacent sequences: A016774 A016775 A016776 this_sequence A016778 A016779 A016780

nonn,easy

njas

Better description from T. D. Noe (noe(AT)sspectra.com), Aug 15 2002