A392137 a(n) = 5*a(n-1) + 2*5^n - 1, a(0) = 0.

0, 9, 94, 719, 4844, 30469, 183594, 1074219, 6152344, 34667969, 192871094, 1062011719, 5798339844, 31433105469, 169372558594, 907897949219, 4844665527344, 25749206542969, 136375427246094, 720024108886719, 3790855407714844, 19907951354980469, 104308128356933594, 545382499694824219

Offset

0,2

Comments

A recurrence relation that occurs in A392135.

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (11,-35,25).

Formula

a(n) = A392135(5^n).

a(n) = 11*a(n-1) - 35*a(n-2) + 25*a(n-3) for n > 2, a(0) = 0, a(1) = 9, a(2) = 94.

a(n) = 2*n*5^n - (5^n - 1)/4. - Jason Yuen, Jan 05 2026

From Enrique Navarrete, Jan 15 2026: (Start)

G.f.: x*(9 - 5*x)/((1 - x)*(1 - 5*x)^2).

E.g.f.: (1/4)*exp(x)*(exp(4*x)*(40*x - 1) + 1). (End)

Mathematica

LinearRecurrence[{11, -35, 25}, {0, 9, 94}, 25] (* Paolo Xausa, Jan 12 2026 *)

Prog

(Python)
def A392137(n):
    if n == 0: return 0
    else: return 5*A392137(n-1) + 2*5**n - 1

Crossrefs

Cf. A392135.

Sequence in context: A231658 A034992 A048359 * A307961 A099297 A057782

Adjacent sequences: A392134 A392135 A392136 * A392138 A392139 A392140

Keyword

nonn,easy

Author

A.H.M. Smeets, Jan 05 2026

Status

approved