A320469 -id:A320469 - cp's OEIS frontend

A321133 a(n) = 3a(n-1) + 10a(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

Seiichi Manyama, Aug 27 2019

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,10).

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

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

PARI
```
{a(n) = 3*5^n-4*(-2)^n}
```

N=40; x='x+O('x^N); Vec((-1+26*x)/((1-5*x)*(1+2*x)))

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.

A320468 a(n) = a(n-1) + 20*a(n-2), n >= 2; a(0)=1, a(1)=41.

Original entry on oeis.org

1, 41, 61, 881, 2101, 19721, 61741, 456161, 1690981, 10814201, 44633821, 260917841, 1153594261, 6371951081, 29443836301, 156882857921, 745759583941, 3883416742361, 18798608421181, 96466943268401, 472439111692021, 2401777977060041, 11850560210900461, 59886119752101281, 296897323970110501

Offset: 0

Seiichi Manyama, Aug 27 2019

Index entries for linear recurrences with constant coefficients, signature (1,20).

Cf. A053428, A224473 (trimorphic number), A320469, A321133.

PARI
```
{a(n) = (-4)^(n+1)+5^(n+1)}
```

N=40; x='x+O('x^N); Vec((1+40*x)/((1-5*x)*(1+4*x)))

a(n) = (-4)^(n+1) + 5^(n+1).
G.f.: (1+40*x)/((1-5*x)*(1+4*x)).
a(n) == 9*A053428(n)*A224473(n) mod 10^n.
a(n)*A224473(n) == 9*A053428(n) mod 10^n.

cp's OEIS Frontend

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

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Formula

A320468 a(n) = a(n-1) + 20*a(n-2), n >= 2; a(0)=1, a(1)=41.

Views

Author

Keywords

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PARI

PARI

Formula

cp's OEIS Frontend

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

PARI

Formula

A320468 a(n) = a(n-1) + 20*a(n-2), n >= 2; a(0)=1, a(1)=41.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

PARI

Formula

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