A118004 -id:A118004 - cp's OEIS frontend

A191465 a(n) = 9^n - 2^n.

0, 7, 77, 721, 6545, 59017, 531377, 4782841, 43046465, 387419977, 3486783377, 31381057561, 282429532385, 2541865820137, 22876792438577, 205891132061881, 1853020188786305, 16677181699535497, 150094635296736977, 1350851717672467801, 12157665459055880225, 109418989131510262057

Offset: 0

Vincenzo Librandi, Jun 03 2011

a(n) is the number of words of length n over the alphabet {1,2,...,9} where at least one letter >= 3 appears. - Joerg Arndt, Jan 18 2024

Vincenzo Librandi, Table of n, a(n) for n = 0..300
Index entries for linear recurrences with constant coefficients, signature (11,-18).

Cf. A016133, A016185, A118004.

Table[9^n-2^n,{n,0,20}] (* Harvey P. Dale, Apr 16 2014 *)

a(n)=9^n-1<Charles R Greathouse IV, Jun 08 2011

a(n) = 11*a(n-1) - 18*a(n-2).
G.f.: 7*x/((1-2*x)*(1-9*x)). - Vincenzo Librandi, Oct 04 2014
a(n) = 7*A016133(n-1). - R. J. Mathar, Mar 10 2022
E.g.f.: 2*exp(11*x/2)*sinh(7*x/2). - Elmo R. Oliveira, Mar 31 2025

A248337 a(n) = 6^n - 4^n.

Original entry on oeis.org

0, 2, 20, 152, 1040, 6752, 42560, 263552, 1614080, 9815552, 59417600, 358602752, 2160005120, 12993585152, 78095728640, 469111242752, 2816814940160, 16909479575552, 101491237191680, 609084862103552, 3655058928435200, 21932552593866752, 131604111656222720, 789659854309425152, 4738099863344906240, 28429162130022858752

Offset: 0

Vincenzo Librandi, Oct 05 2014

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (10,-24).

Cf. sequences of the form k^n - 4^n: -A000302 (k=0), -A024036 (k=1), -A020522 (k=2), -A005061 (k=3), A005060 (k=5), this sequence (k=6), A190542 (k=7), A059409 (k=8), A118004 (k=9), A248338 (k=10), A139742 (k=11), 8*A016159 (k=12).

Cf. A000079, A000302, A000400, A001047, A081199.

Magma
```
[6^n-4^n: n in [0..30]];
```

Table[6^n - 4^n, {n,0,30}]
CoefficientList[Series[(2 x)/((1-4 x)(1-6 x)), {x, 0, 30}], x]
LinearRecurrence[{10,-24},{0,2},30] (* Harvey P. Dale, Aug 18 2024 *)

vector(20,n,6^(n-1)-4^(n-1)) \\ Derek Orr, Oct 05 2014

A248337=BinaryRecurrenceSequence(10,-24,0,2)
[A248337(n) for n in range(31)] # G. C. Greubel, Nov 11 2024

G.f.: 2*x/((1-4*x)*(1-6*x)).
a(n) = 10*a(n-1) - 24*a(n-2).
a(n) = 2^n*(3^n-2^n) =  A000079(n) * A001047(n) = A000400(n) - A000302(n).
a(n) = 2*A081199(n). - Bruno Berselli, Oct 05 2014
E.g.f.: 2*exp(5*x)*sinh(x). - G. C. Greubel, Nov 11 2024

More terms added by G. C. Greubel, Nov 11 2024

A191466 a(n) = 9^n - 5^n.

Original entry on oeis.org

0, 4, 56, 604, 5936, 55924, 515816, 4704844, 42656096, 385467364, 3477018776, 31332231484, 282185395856, 2540645125204, 22870688939336, 205860614516524, 1852867600961216, 16676418760213444, 150090820599733496, 1350832644186663964, 12157570091625288176, 109418512294354156084

Offset: 0

Vincenzo Librandi, Jun 03 2011

Vincenzo Librandi, Table of n, a(n) for n = 0..300
Index entries for linear recurrences with constant coefficients, signature (14,-45).

Cf. A016163, A016185, A059410, A118004.

Magma
```
[9^n-5^n: n in [0..20]];
```

Table[9^n - 5^n, {n, 0, 25}] (* or *) CoefficientList[Series[4 x/((1 - 5 x) (1 - 9 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 05 2014 *)
LinearRecurrence[{14,-45},{0,4},20] (* Harvey P. Dale, Jun 26 2019 *)

a(n)=9^n-5^n \\ Charles R Greathouse IV, Jun 08 2011

a(n) = 14*a(n-1) - 45*a(n-2).
From Vincenzo Librandi, Oct 05 2014: (Start)
G.f.: 4*x/((1-5*x)*(1-9*x)).
a(n+1) = 4*A016163(n). (End)
E.g.f.: 2*exp(14*x/2)*sinh(2*x). - Elmo R. Oliveira, Mar 31 2025

A191467 9^n - 7^n.

Original entry on oeis.org

0, 2, 32, 386, 4160, 42242, 413792, 3959426, 37281920, 347066882, 3204309152, 29403732866, 268588249280, 2444976817922, 22198569382112, 201143570584706, 1819787258282240, 16444551185679362, 148466221699088672, 1339452822487618946

Offset: 0

Vincenzo Librandi, Jun 03 2011

Vincenzo Librandi, Table of n, a(n) for n = 0..300
Index entries for linear recurrences with constant coefficients, signature (16,-63).

Cf. A118004, A016178, A016185, A059410, A139745, A191467.

Magma
```
[9^n - 7^n: n in [0..20]]:
```

Table[9^n-7^n,{n,0,20}] (* or *) LinearRecurrence[{16,-63},{0,2},20] (* Harvey P. Dale, Jun 21 2014 *)
CoefficientList[Series[2 x/((1 - 7 x) (1 - 9 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 05 2014 *)

a(n)=9^n-7^n \\ Charles R Greathouse IV, Jun 08 2011

a(n) = 16*a(n-1) - 63*a(n-2).
G.f.: 2*x/((1-7*x)*(1-9*x)). - Vincenzo Librandi, Oct 05 2014
a(n+1) = 2*A016178(n). - Vincenzo Librandi, Oct 05 2014

A167536 a(n) = 3^(2^n) - 2^(2^n).

Original entry on oeis.org

1, 5, 65, 6305, 42981185, 1853015893884545, 3433683820274065740584139537665, 11790184577738583171520532579045597727214748217668409340885505

Offset: 0

Jamel Ghanouchi, Nov 06 2009

nonn

Cf. A118004.

[3^(2^n)-2^(2^n): n in [0..10]]; // Vincenzo Librandi Jun 15 2016

A167536 := proc(n) 3^(2^n)-2^(2^n) ; end proc: seq(A167536(n),n=1..10) ; # R. J. Mathar, Nov 07 2009

a[n_]:= 2^n; Table[3^a[n] - 2^a[n], {n, 0, 10}] (* G. C. Greubel, Jun 14 2016 *)
Table[3^(2^n) - 2^(2^n), {n, 0, 10}] (* Vincenzo Librandi, Jun 15 2016 *)

a(n)= A001047(2^n).

Edited by R. J. Mathar, Nov 11 2009

Offset changed from 1 to 0 from Vincenzo Librandi, Jun 15 2016

cp's OEIS Frontend

A191465 a(n) = 9^n - 2^n.

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A248337 a(n) = 6^n - 4^n.

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A191466 a(n) = 9^n - 5^n.

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A191467 9^n - 7^n.

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A167536 a(n) = 3^(2^n) - 2^(2^n).

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