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

Author

Clark Kimberling

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A027960.

Programs

Magma

A027982:= func< n | (2*n+11)*2^n -2*(3*n+5) >; // G. C. Greubel, Jun 07 2025

Mathematica

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

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

Python

def A027982(n): return (2*n+11)*2**n -2*(3*n+5) # G. C. Greubel, Jun 07 2025

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

Extensions

More terms from Colin Barker, Nov 25 2014