A321133 a(n) = 3*a(n-1) + 10*a(n-2), n >= 2; a(0)=-1, a(1)=23.

-1, 23, 59, 407, 1811, 9503, 46619, 234887, 1170851, 5861423, 29292779, 146492567, 732405491, 3662142143, 18310481339, 91552865447, 457763409731, 2288818883663, 11444090748299, 57220461081527, 286102290727571, 1430511482997983, 7152557356269659, 35762786898788807, 178813934259063011

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,10).

Formula

a(n) = 3*5^n - 4*(-2)^n.

G.f.: (-1+26*x)/((1-5*x)*(1+2*x)).

a(n) == 7*A320469(n)*A224473(n) mod 10^n.

a(n)*A224473(n) == 7*A320469(n) mod 10^n.

Mathematica

LinearRecurrence[{3, 10}, {-1, 23}, 30] (* Harvey P. Dale, Mar 11 2023 *)

Prog

(PARI) {a(n) = 3*5^n-4*(-2)^n}
(PARI) N=40; x='x+O('x^N); Vec((-1+26*x)/((1-5*x)*(1+2*x)))

Crossrefs

Cf. A053428, A224473 (trimorphic number), A320468, A320469.

Sequence in context: A142107 A107208 A289735 * A055821 A080822 A068363

Adjacent sequences: A321130 A321131 A321132 * A321134 A321135 A321136

Keyword

sign,easy

Author

Seiichi Manyama, Aug 27 2019

Status

approved