A101892 a(n) = Sum_{k=0..floor(n/2)} binomial(n,2*k)*J(k), where J = A001045.

0, 0, 1, 3, 7, 15, 33, 77, 187, 459, 1121, 2717, 6555, 15795, 38081, 91893, 221867, 535755, 1293633, 3123277, 7540187, 18203139, 43945441, 106092997, 256131435, 618357915, 1492851361, 3604064733, 8700980827, 21006018195, 50713000833

Offset: 0

Author

Paul Barry, Dec 22 2004

Keywords

• easy
• nonn

Comments

Transform of A001045 under the mapping g(x)-> (1/(1-x))*g(x^2/((1-x)^2)). Binomial transform of aerated Jacobsthal numbers 0,0,1,0,1,0,3,0,5,0,11,...

J(n) may be recovered as Sum_{k=0..2*n} Sum_{j=0..k} C(0,2*n-k)*C(k,j)*(-1)^(k-j)*a(j). - Paul Barry, Jun 10 2005

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-5,2,2).

Crossrefs

Cf. A001045, A001333, A009545.

Formula

G.f.: x^2*(1 - x)/((1 - 2*x - x^2)*(1 - 2*x + 2*x^2)).

a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) + 2*a(n-4).

a(n) = Sum_{k=0..n} binomial(n, k)*A001045(k/2)*(1+(-1)^k)/2.

a(n) = (1/6)*( 2*A001333(n) - A009545(n+2) ). - Ralf Stephan, May 17 2007