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

0,1

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).

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).

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]

Prog

(Magma)
R<x>:=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
(Sage)
def A168823_list(prec):
    P.<x> = 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

Crossrefs

Cf. A074062, A074825.

Sequence in context: A217706 A064864 A004553 * A018246 A101101 A046786

Adjacent sequences: A074823 A074824 A074825 * A074827 A074828 A074829

Keyword

easy,sign

Author

Mario Catalani (mario.catalani(AT)unito.it), Sep 10 2002

Status

approved