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, 44114542592, 142757658624, 230986743808
Offset: 0
Examples
Sequence begins: {1*1, 1*2, 2*2, 3*4, 5*4, 8*8, 13*8, 21*16, 34*16, ...}.
Links
- Stefano Spezia, Table of n, a(n) for n = 0..2500
- Index entries for linear recurrences with constant coefficients, signature (0,6,0,-4).
Programs
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Mathematica
LinearRecurrence[{0,6,0,-4},{1,2,4,12},30] (* Harvey P. Dale, Aug 09 2016 *) -
PARI
a(n)=fibonacci(n+1)*2^((n+1)\2)
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).