A075129 Binomial transform of reflected tetranacci numbers A074058: a(n)=Sum((-1)^k Binomial(n,k)*A074058(k),(k=0,..,n)).
4, 5, 5, 5, 13, 50, 155, 390, 861, 1805, 3850, 8640, 20167, 47520, 110780, 254450, 579149, 1316485, 3003095, 6878765, 15790278, 36245235, 83101760, 190322935, 435678591, 997445500, 2284365660, 5233190405, 11989714652, 27467989310
Offset: 0
Links
- N. J. A. Sloane, Transforms
- Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -3).
Programs
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Mathematica
CoefficientList[Series[(4-15*z+20*z^2-10*z^3)/(1-5*z+10*z^2-10*z^3+3*z^4), {z, 0, 30}], z] LinearRecurrence[{5,-10,10,-3},{4,5,5,5},30] (* Harvey P. Dale, Jan 26 2025 *)
Formula
a(n)=5a(n-1)-10a(n-2)+10a(n-3)-3a(n-4), a(0)=4, a(1)=5, a(2)=5, a(3)=5. G.f.: (4 - 15*z + 20*z^2 - 10*z^3)/(1 - 5*z + 10*z^2 - 10*z^3 + 3*z^4).