A093146 Third binomial transform of Pell(3n-1).

1, 5, 50, 750, 12500, 212500, 3625000, 61875000, 1056250000, 18031250000, 307812500000, 5254687500000, 89703125000000, 1531328125000000, 26141406250000000, 446261718750000000, 7618164062500000000, 130050195312500000000, 2220095703125000000000, 37899404296875000000000

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.: (1-15*x)/(1 - 20*x + 50*x^2);

a(n) = (10 + 5*sqrt(2))^n*(1/2 - sqrt(2)/4) + (10 - 5*sqrt(2))^n*(1/2 + sqrt(2)/4).

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

Mathematica

LinearRecurrence[{20, -50}, {1, 5}, 27] (* Amiram Eldar, Jan 25 2026 *)

Crossrefs

Cf. A000129, A093144, A093147.

Sequence in context: A217794 A347022 A381262 * A049393 A047054 A052562

Adjacent sequences: A093143 A093144 A093145 * A093147 A093148 A093149

Keyword

easy,nonn

Author

Paul Barry, Mar 26 2004

Extensions

More terms from Amiram Eldar, Jan 25 2026

Status

approved