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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. 7
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified November 19 20:42 EST 2019. Contains 329323 sequences. (Running on oeis4.)