A141495 -id:A141495 - cp's OEIS frontend

A141496 a(0)=1; a(1)=5; a(2)=11; a(n)=a(1)*a(n-1).

1, 5, 11, 55, 275, 1375, 6875, 34375, 171875, 859375, 4296875, 21484375, 107421875, 537109375, 2685546875, 13427734375, 67138671875, 335693359375, 1678466796875, 8392333984375, 41961669921875, 209808349609375

Offset: 0

Roger L. Bagula, Aug 10 2008

Index entries for linear recurrences with constant coefficients, signature (5).

Cf. A084215, A141495.

Clear[a] a[0] = 1; a[1] = 5; a[2] = 11; a[n_] := a[n] = a[1]*a[n - 1]; Table[a[n], {n, 0, 30}]

a(n) = 11*5^(n-2) for n>1. a(n) = 5*a(n-1) for n>2. G.f.: (1-14*x^2)/(1-5*x). [Colin Barker, Oct 13 2012]

Edited by N. J. A. Sloane, Aug 16 2008

A308124 a(n) = (2 + 7*4^n)/3.

Original entry on oeis.org

3, 10, 38, 150, 598, 2390, 9558, 38230, 152918, 611670, 2446678, 9786710, 39146838, 156587350, 626349398, 2505397590, 10021590358, 40086361430, 160345445718, 641381782870, 2565527131478, 10262108525910, 41048434103638, 164193736414550, 656774945658198, 2627099782632790

Offset: 0

Paul Curtz, Jul 23 2019

Consider A092808 and its differences:
1,  0,  3,  1, 11,  5,  43,  21, 171, ...
-1, 3, -2, 10, -6, 38, -22, 150, ... = b(n).
a(n) is the second bisection of b(n). The first is A047849.
a(n) mod 9 is the period 9 sequence: repeat [3, 1, 2, 6, 4, 5, 0, 7, 8].
b(n) + b(n+1) = A135520(n).

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-4).

Cf. A000302, A001045, A002042, A092808, A047849, A135520, A141495.

LinearRecurrence[{5,-4},{3,10},30] (* Paolo Xausa, Nov 13 2023 *)
(2+7*4^Range[0,30])/3 (* Harvey P. Dale, Aug 15 2025 *)

a(n) = (2 + 7*4^n)/3; \\ Stefano Spezia, Jul 23 2019

Vec((3 - 5*x) / ((1 - x)*(1 - 4*x)) + O(x^40)) \\ Colin Barker, Jul 23 2019

a(n) = 4*a(n-1) - 2 for n=1,2,... , a(0) = 3.
a(n+1) = a(n) + A002042(n).
Binomial transform of A141495(n+1) = 3, 7, 21, ....
From Colin Barker, Jul 23 2019: (Start)
G.f.: (3 - 5*x) / ((1 - x)*(1 - 4*x)).
a(n) = 5*a(n-1) - 4*a(n-2) for n>1.
(End)
a(n+2) = a(n) + 35*A000302(n) for n=0,1,2, ... .

a(14)-a(25) from Stefano Spezia, Jul 23 2019

cp's OEIS Frontend

A141496 a(0)=1; a(1)=5; a(2)=11; a(n)=a(1)*a(n-1).

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