A099603 Row sums of triangle A099602, in which row n equals the inverse binomial transform of column n of the triangle of trinomial coefficients (A027907).

1, 2, 4, 12, 20, 64, 104, 336, 544, 1760, 2848, 9216, 14912, 48256, 78080, 252672, 408832, 1323008, 2140672, 6927360, 11208704, 36272128, 58689536, 189923328, 307302400, 994451456, 1609056256, 5207015424, 8425127936, 27264286720

Offset

0,2

Links

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (0,6,0,-4).

Formula

a(n) = fibonacci(n+1)*2^[(n+1)/2]. a(n) = 6*a(n-2) - 4*a(n-4) for n>4. G.f.: (1+2*x-2*x^2)/(1-6*x^2+4*x^4).

Example

Sequence begins: {1*1, 1*2, 2*2, 3*4, 5*4, 8*8, 13*8, 21*16, 34*16, ...}.

Mathematica

LinearRecurrence[{0, 6, 0, -4}, {1, 2, 4, 12}, 30] (* Harvey P. Dale, Aug 09 2016 *)

Prog

(PARI) a(n)=fibonacci(n+1)*2^((n+1)\2)

Crossrefs

Cf. A000045, A099602.

Sequence in context: A218871 A121569 A319213 * A319615 A343865 A062767

Adjacent sequences: A099600 A099601 A099602 * A099604 A099605 A099606

Keyword

nonn

Author

Paul D. Hanna, Oct 25 2004

Status

approved