A074826 Binomial transform of reflected pentanacci numbers A074062: a(n) = Sum_{k=0..n}(-1)^k*binomial(n, k)*A074062(k).
5, 6, 6, 6, 6, -4, -60, -246, -722, -1758, -3754, -7144, -11868, -15646, -9458, 32726, 174750, 555668, 1446564, 3310642, 6788406, 12366066, 19107358, 21047904, -1585148, -101419654, -400928730, -1155269658, -2838111242, -6203242964, -12144929980, -20857830310, -29087301442
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- N. J. A. Sloane, Transforms
- Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,4).
Programs
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Magma
R
:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (5-24*x+45*x^2-40*x^3+15*x^4)/(1-6*x+15*x^2-20*x^3+15*x^4 -4*x^5) )); // G. C. Greubel, Jul 08 2021 -
Mathematica
CoefficientList[Series[(5-24x+45x^2-40x^3+15x^4)/(1-6x+15x^2-20x^3+15x^4-4x^5), {x, 0, 35}], x] -
Sage
def A168823_list(prec): P.
= PowerSeriesRing(ZZ, prec) return P( (5-24*x+45*x^2-40*x^3+15*x^4)/(1-6*x+15*x^2-20*x^3+15*x^4-4*x^5) ).list() A168823_list(40) # G. C. Greubel, Jul 08 2021
Formula
a(n) = Sum_{j=0..n} (-1)^j*binomial(n, j)*A074062(j)
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 4*a(n-5), a(0) = 5, a(1) = 6, a(2) = 6, a(3) = 6, a(4) = 6.
G.f.: (5 -24*x +45*x^2 -40*x^3 +15*x^4)/(1 -6*x +15*x^2 -20*x^3 +15*x^4 -4*x^5).