A092687 First column and main diagonal of triangle A092686, in which the convolution of each row with {1,2} produces a triangle that, when flattened, equals the flattened form of A092686.

1, 2, 6, 16, 46, 132, 384, 1120, 3278, 9612, 28236, 83072, 244752, 722048, 2132704, 6306304, 18666190, 55300732, 163968612, 486528288, 1444571068, 4291629384, 12756459936, 37934818112, 112855778768, 335867740704, 999895548736

Offset

0,2

Comments

Conjecture: Limit n->infinity a(n)^(1/n) = 3. - Vaclav Kotesovec, Jun 29 2015

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..850

Formula

G.f. satisfies: A(x) = A( x^2/(1-2x) )/(1-2x). Recurrence: a(n) = Sum_{k=0..floor(n/2)} C(n-k,k)*2^(n-2k)*a(k). - Paul D. Hanna, Jul 10 2006

Mathematica

m = 27; A[_] = 1; Do[A[x_] = A[x^2/(1-2x)]/(1-2x) + O[x]^m // Normal, {m}]; CoefficientList[A[x], x] (* Jean-François Alcover, Nov 03 2019 *)

Prog

(PARI) T(n, k)=if(n<0||k>n, 0, if(n==0&k==0, 1, if(n==1&k<=1, 2, if(k==n, T(n, 0), 2*T(n-1, k)+T(n-1, k+1)))))
a(n)=T(n, 0)
for(n=0, 30, print1(a(n), ", "))
(PARI) a(n)=local(A=1+x); for(i=0, n\2, A=subst(A, x, x^2/(1-2*x+x*O(x^n)))/(1-2*x)); polcoeff(A, n) \\ Paul D. Hanna, Jul 10 2006
(PARI) /* Using Recurrence: */
a(n)=if(n==0, 1, sum(k=0, n\2, binomial(n-k, k)*2^(n-2*k)*a(k)))
for(n=0, 30, print1(a(n), ", ")) \\ Paul D. Hanna, Jul 10 2006

Crossrefs

Cf. A092683, A092686, A092688, A092689.

Sequence in context: A307606 A098617 A291036 * A094039 A165431 A182267

Adjacent sequences: A092684 A092685 A092686 * A092688 A092689 A092690

Keyword

nonn

Author

Paul D. Hanna, Mar 04 2004

Status

approved