0,2

Second differences are all 3.

Related to the sequence of odd numbers A005408 since for these numbers the first differences are all 2.

Column 2 of A114202. - Paul Barry (pbarry(AT)wit.ie), Nov 17 2005

Thomas Wieder, Home Page.

Thomas Wieder, (Old) Home Page.

G.f.: (1+2*x^2)/(1-3*x+3*x^2-x^3), recurrence: {u(1) = 3, u(2) = 8, (n+3)*u(n+3)+(-5-n)*u(n+2)+(-2+2*n)*u(n+1)+(-2-2*n)*u(n), u(0) = 1}.

a(0)=1, a(n)=a(n-1)+3n-1, n>0; a(n)=sum{k=0..n, C(n, k)C(2, k)J(k+1)}, J(n)=A001045(n). - Paul Barry (pbarry(AT)wit.ie), Nov 17 2005

Equals binomial transform of [1, 2, 3, 0, 0, 0,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 23 2008

Equals binomial transform of [1, 2, 3, 0, 0, 0,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), May 04 2008

a(n)=3*n+a(n-1)-4 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009]

The sequence of first differences delta_a(n) = a(n+1) - a(n) is

2,5,8,11,14,17,20,23,26,...

The sequence of second differences delta_delta_a(n) = a(n+2) - 2*a(n+1) + a(n) is

3,3,3,3,3,3,3,3,3,...

E.g. 78 - 2*58 + 41 = 3.

For n=2, a(2)=3*2+1-4=3; n=3, a(3)=3*3+3-4=8; n=4, a(4)=3*4+8-4=16 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009]

a := proc (n) local i, u; option remember; u[0] := 1; u[1] := 3; u[2] := 8; for i from 3 to n do u[i] := -(4*u[i-3]-8*u[i-2]-2*u[i-1]+(-2*u[i-3]+2*u[i-2]-u[i-1])*i)/i end do; [seq(u[i], i = 0 .. n)] end proc;

Cf. A005408, A016777, A002597, A001399.

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Nov 12 2009: (Start)

Equals third row of A167560 divided by 2.

(End)

Sequence in context: A122794 A115006 A122796 this_sequence A025202 A131941 A009858

Adjacent sequences: A104246 A104247 A104248 this_sequence A104250 A104251 A104252

easy,nonn,new

Thomas Wieder (wieder.thomas(AT)t-online.de), Feb 26 2005

More terms a(31)-a(46) from Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009