A093144 Third binomial transform of Pell(3*n)/Pell(3).

0, 1, 20, 350, 6000, 102500, 1750000, 29875000, 510000000, 8706250000, 148625000000, 2537187500000, 43312500000000, 739390625000000, 12622187500000000, 215474218750000000, 3678375000000000000, 62793789062500000000, 1071957031250000000000, 18299451171875000000000

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (20,-50).

Formula

G.f.: x/(1-20*x+50*x^2);

a(n) = ((10 + 5*sqrt(2))^n - (10 - 5*sqrt(2))^n)/(10*sqrt(2)).

E.g.f.: exp(10*x) * sinh(5*sqrt(2)*x) / (5*sqrt(2)). - Amiram Eldar, Jan 15 2026

Mathematica

LinearRecurrence[{20, -50}, {0, 1}, 30] (* Harvey P. Dale, Aug 04 2021 *)

Crossrefs

Cf. A000129, A041085.

Sequence in context: A272183 A005748 A230236 * A285393 A156455 A358365

Adjacent sequences: A093141 A093142 A093143 * A093145 A093146 A093147

Keyword

easy,nonn

Author

Paul Barry, Mar 26 2004

Status

approved