A086605 a(n) = 9*n^3 - 18*n^2 + 10*n.

0, 1, 20, 111, 328, 725, 1356, 2275, 3536, 5193, 7300, 9911, 13080, 16861, 21308, 26475, 32416, 39185, 46836, 55423, 65000, 75621, 87340, 100211, 114288, 129625, 146276, 164295, 183736, 204653, 227100, 251131, 276800, 304161, 333268, 364175

Offset

0,3

Comments

Binomial transform is A086604.

Second binomial transform is 3^(n-1)*n^3 = A086603(n).

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

G.f.: x*(1 + 16*x + 37*x^2)/(1-x)^4.

a(0)=0, a(1)=1, a(2)=20, a(3)=111, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Harvey P. Dale, Mar 05 2013

E.g.f.: x*(1 + 9*x + 9*x^2)*exp(x). - G. C. Greubel, Feb 08 2020

Maple

seq( 9*n^3 - 18*n^2 + 10*n, n=0..40); # G. C. Greubel, Feb 08 2020

Mathematica

Table[9n^3-18n^2+10n, {n, 0, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 1, 20, 111}, 40] (* Harvey P. Dale, Mar 05 2013 *)

Prog

(PARI) vector(41, n, my(m=n-1); 9*m^3 - 18*m^2 + 10*m) \\ G. C. Greubel, Feb 08 2020
(Magma) [9*n^3 - 18*n^2 + 10*n: n in [0..40]]; // G. C. Greubel, Feb 08 2020
(SageMath) [9*n^3 - 18*n^2 + 10*n for n in (0..40)] # G. C. Greubel, Feb 08 2020
(GAP) List([0..40], n-> n*(1 + 9*(n-1)^2) ); # G. C. Greubel, Feb 08 2020

Crossrefs

Cf. A086603, A086604.

Sequence in context: A380985 A309781 A228243 * A321050 A107837 A267843

Adjacent sequences: A086602 A086603 A086604 * A086606 A086607 A086608

Keyword

easy,nonn

Author

Paul Barry, Jul 23 2003

Status

approved