A027981 a(n) = Sum_{k=0..2*n} (k+1)*T(n,k), T given by A027960.

1, 10, 40, 124, 340, 868, 2116, 4996, 11524, 26116, 58372, 129028, 282628, 614404, 1327108, 2850820, 6094852, 12976132, 27525124, 58195972, 122683396, 257949700, 541065220, 1132462084, 2365587460, 4932501508, 10267656196, 21340618756, 44291850244, 91804925956, 190052302852, 392989507588, 811748818948, 1675037245444, 3453153705988

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-8,4).

Crossrefs

Cf. A027960.

Programs

Magma

A027981:= func< n | 3*2^n*(2*n-1) + 4 >; // G. C. Greubel, Jun 07 2025

Mathematica

LinearRecurrence[{5,-8,4},{1,10,40},30] (* Harvey P. Dale, Apr 17 2015 *)

Python

def A027981(n): return 3*2**n*(2*n-1) + 4 # G. C. Greubel, Jun 07 2025

Formula

a(2*n+1) = 6*(4*n+1) * 4^n + 4. - Ralf Stephan, Mar 22 2004

From R. J. Mathar, May 22 2013: (Start)

a(n) = 3*2^n*(2*n-1) + 4.

G.f.: (1 + 5*x - 2*x^2)/( (1-x)*(1-2*x)^2 ). (End)

a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3), with a(0)=1, a(1)=10, a(2)=40. - Harvey P. Dale, Apr 17 2015

E.g.f.: 3*(4*x - 1)*exp(2*x) + 4*exp(x). - Ilya Gutkovskiy, Apr 17 2016

Extensions

More terms added by G. C. Greubel, Jun 07 2025