A093147 Third binomial transform of Pell(3n+1).

1, 15, 250, 4250, 72500, 1237500, 21125000, 360625000, 6156250000, 105093750000, 1794062500000, 30626562500000, 522828125000000, 8925234375000000, 152363281250000000, 2601003906250000000, 44401914062500000000, 757988085937500000000, 12939666015625000000000, 220893916015625000000000

Offset

0,2

Links

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

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

Formula

G.f.: (1-5*x)/(1 - 20*x + 50*x^2).

a(n) = ((1 + sqrt(2))*(10 + 5*sqrt(2))^n - (1 - sqrt(2))*(10-5*sqrt(2))^n)/(2*sqrt(2)).

E.g.f.: exp(10*x) * (cosh(5*sqrt(2)*x) + sinh(5*sqrt(2)*x)/sqrt(2)). - Amiram Eldar, Jan 25 2026

a(n) = 20*a(n-1) - 50*a(n-2). - Wesley Ivan Hurt, Jun 05 2026

Mathematica

LinearRecurrence[{20, -50}, {1, 15}, 27] (* Amiram Eldar, Jan 25 2026 *)

Crossrefs

Cf. A000129, A093144, A093146.

Sequence in context: A218806 A285395 A331493 * A218192 A066410 A370317

Adjacent sequences: A093144 A093145 A093146 * A093148 A093149 A093150

Keyword

easy,nonn,changed

Author

Paul Barry, Mar 26 2004

Extensions

More terms from Amiram Eldar, Jan 25 2026

Status

approved