A074825 Binomial transform of reflected pentanacci numbers A074062: a(n) = Sum_{k=0..n} binomial(n,k)*A074062(k).

5, 4, 2, -2, -10, -16, -4, 46, 142, 250, 262, 4, -652, -1530, -1818, 38, 5662, 14760, 22028, 15014, -22490, -95846, -172434, -154740, 110500, 733134, 1556206, 1875238, 365334, -4306496, -11734244, -17112802, -9496002, 25050298, 90586134, 157886356, 142006676, -87803882

Offset: 0

Author

Mario Catalani (mario.catalani(AT)unito.it), Sep 09 2002

Keywords

• easy
• sign

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 (4,-7,6,-3,2).

Crossrefs

Cf. A074062.

Programs

Magma

I:=[5,4,2,-2,-10]; [n le 5 select I[n] else 4*Self(n-1) -7*Self(n-2) +6*Self(n-3) -3*Self(n-4) +2*Self(n-5): n in [1..51]]; // G. C. Greubel, Jul 05 2021

Mathematica

CoefficientList[Series[(5-16x+21x^2-12x^3+3x^4)/(1-4x+7x^2-6x^3+3x^4-2x^5), {x, 0, 40}], x]
LinearRecurrence[{4,-7,6,-3,2},{5,4,2,-2,-10},40] (* Harvey P. Dale, Nov 29 2019 *)

Sage

def A074825_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (5-16*x+21*x^2-12*x^3+3*x^4)/(1-4*x+7*x^2-6*x^3+3*x^4-2*x^5) ).list()
A074825_list(50) # G. C. Greubel, Jul 05 2021

Formula

a(n) = 4*a(n-1) - 7*a(n-2) + 6*a(n-3) - 3*a(n-4) + 2*a(n-5), a(0)=5, a(1)=4, a(2)=2, a(3)=-2, a(4)=-10.

G.f.: (5 -16*x +21*x^2 -12*x^3 +3*x^4)/(1 -4*x +7*x^2 -6*x^3 +3*x^4 -2*x^5).