OFFSET
0,2
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..1000
FORMULA
Equals the self-convolution of A073707.
EXAMPLE
G.f.: A(x) = 1 + 2*x + 5*x^2 + 8*x^3 + 18*x^4 + 28*x^5 + 50*x^6 +...
where A(x)^2 = 1 + 4*x + 14*x^2 + 36*x^3 + 93*x^4 + 208*x^5 + 456*x^6 +...
This sequence equals the self-convolution of A073707, which begins:
[1, 1, 2, 2, 5, 5, 8, 8, 18, 18, 28, 28, 50, 50, ...].
The first differences of this sequence result in A073709:
[1, 1, 3, 3, 10, 10, 22, 22, 57, 57, 115, 115, ...];
[1, 2, 7, 12, 35, 58, 133, 208, ...],
which in turn equals the first differences of the unique terms of A073709.
MATHEMATICA
A073708list[n_] := Module[{m = 1, A = 1}, While[m <= n, m = 2 m; A = ((1 + x)*(A /. x -> x^2))^2] + O[x]^m; CoefficientList[A, x][[1 ;; n]]]; A073708list[50] (* Jean-François Alcover, Apr 21 2016, adapted from PARI *)
PROG
(PARI) a(n)=local(A, m); if(n<0, 0, m=1; A=1+O(x); while(m<=n, m*=2; A=((1+x)*subst(A, x, x^2))^2); polcoeff(A, n))
(Haskell)
a073708 n = a073708_list !! n
a073708_list = conv a073707_list [] where
conv (v:vs) ws = (sum $ zipWith (*) ws' $ reverse ws') : conv vs ws'
where ws' = v : ws
-- Reinhard Zumkeller, Jun 13 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul D. Hanna, Aug 04 2002
EXTENSIONS
Edited by Michael Somos, May 03, 2003
Edited by Paul D. Hanna, Jan 04 2013
STATUS
approved