A027982 a(n) = Sum_{k=0..2*n} (k+1)*T(n, 2*n-k), T given by A027960.

1, 10, 38, 108, 270, 632, 1426, 3148, 6854, 14784, 31674, 67508, 143278, 303016, 638882, 1343388, 2817942, 5898128, 12320650, 25689988, 53477246, 111148920, 230686578, 478150508, 989855590, 2046820192, 4227858266, 8724152148, 17985175374, 37044092744

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-13,12,-4).

Formula

From Colin Barker, Nov 25 2014: (Start)

a(n) = (-10 + 11*2^n + 2*(-3 + 2^n)*n).

a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4).

G.f.: (1 + 4*x - 9*x^2 - 2*x^3) / ((1-x)^2*(1-2*x)^2). (End)

E.g.f.: (11 + 4*x)*exp(2*x) - 2*(5 + 3*x)*exp(x). - G. C. Greubel, Jun 07 2025

Mathematica

LinearRecurrence[{6, -13, 12, -4}, {1, 10, 38, 108}, 40] (* Harvey P. Dale, Oct 28 2020 *)

Prog

(PARI) Vec((1+4*x-9*x^2-2*x^3)/((1-x)^2*(1-2*x)^2) + O(x^100)) \\ Colin Barker, Nov 25 2014
(Magma)
A027982:= func< n | (2*n+11)*2^n -2*(3*n+5) >; // G. C. Greubel, Jun 07 2025
(Python)
def A027982(n): return (2*n+11)*2**n -2*(3*n+5) # G. C. Greubel, Jun 07 2025

Crossrefs

Cf. A027960.

Sequence in context: A257051 A250420 A136840 * A064603 A164298 A050479

Adjacent sequences: A027979 A027980 A027981 * A027983 A027984 A027985

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

More terms from Colin Barker, Nov 25 2014

Status

approved