A009988 -id:A009988 - cp's OEIS frontend

A009966 Powers of 22.

1, 22, 484, 10648, 234256, 5153632, 113379904, 2494357888, 54875873536, 1207269217792, 26559922791424, 584318301411328, 12855002631049216, 282810057883082752, 6221821273427820544, 136880068015412051968, 3011361496339065143296, 66249952919459433152512, 1457498964228107529355264, 32064977213018365645815808, 705429498686404044207947776

Offset: 0

N. J. A. Sloane

Same as Pisot sequences E(1, 22), L(1, 22), P(1, 22), T(1, 22). Essentially same as Pisot sequences E(22, 484), L(22, 484), P(22, 484), T(22, 484). See A008776 for definitions of Pisot sequences.

The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n>=1, a(n) equals the number of 22-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

T. D. Noe, Table of n, a(n) for n = 0..100
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (22).

Cf. A000079, A001020, A008776, A009988.

[22^n: n in [0..100]]; // Vincenzo Librandi, Nov 21 2010

NestList[22#&,1,20] (* Harvey P. Dale, Apr 22 2022 *)

a(n)=22^n \\ Charles R Greathouse IV, Oct 07 2015

[lucas_number1(n,22,0) for n in range(1, 17)] # Zerinvary Lajos, Apr 29 2009

G.f.: 1/(1-22*x). - Philippe Deléham, Nov 23 2008
a(n) = 22^n; a(n) = 22*a(n-1) n>0 a(0)=1. - Vincenzo Librandi, Nov 21 2010
From Elmo R. Oliveira, Jul 08 2025: (Start)
E.g.f.: exp(22*x).
a(n) = A000079(n)*A001020(n) = A009988(n)/A000079(n). (End)

A218747 a(n) = (44^n - 1)/43.

Original entry on oeis.org

0, 1, 45, 1981, 87165, 3835261, 168751485, 7425065341, 326702875005, 14374926500221, 632496766009725, 27829857704427901, 1224513738994827645, 53878604515772416381, 2370658598693986320765, 104308978342535398113661, 4589595047071557517001085, 201942182071148530748047741

Offset: 0

M. F. Hasler, Nov 04 2012

Partial sums of powers of 44 (A009988).

Vincenzo Librandi, Table of n, a(n) for n = 0..600
Index entries related to partial sums.
Index entries related to q-numbers.
Index entries for linear recurrences with constant coefficients, signature (45,-44).

Cf. similar sequences of the form (k^n-1)/(k-1): A000225, A003462, A002450, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A091030, A135519, A135518, A131865, A091045, A218721, A218722, A064108, A218724-A218734, A132469, A218736-A218753, A133853, A094028, A218723.

Cf. A009988.

[n le 2 select n-1 else 45*Self(n-1) - 44*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012

LinearRecurrence[{45, -44}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)
Join[{0},Accumulate[44^Range[0,20]]] (* Harvey P. Dale, Dec 28 2015 *)

A218747(n):=(44^n-1)/43$
makelist(A218747(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

PARI
```
A218747(n)=44^n\43
```

From Vincenzo Librandi, Nov 07 2012: (Start)
G.f.: x/((1-x)*(1-44*x)).
a(n) = 45*a(n-1) - 44*a(n-2).
a(n) = floor(44^n/43). (End)
E.g.f.: exp(x)*(exp(43*x) - 1)/43. - Elmo R. Oliveira, Aug 29 2024

A165865 Totally multiplicative sequence with a(p) = 44.

Original entry on oeis.org

1, 44, 44, 1936, 44, 1936, 44, 85184, 1936, 1936, 44, 85184, 44, 1936, 1936, 3748096, 44, 85184, 44, 85184, 1936, 1936, 44, 3748096, 1936, 1936, 85184, 85184, 44, 85184, 44, 164916224, 1936, 1936, 1936, 3748096, 44, 1936, 1936, 3748096, 44, 85184, 44

Offset: 1

Jaroslav Krizek, Sep 28 2009

G. C. Greubel, Table of n, a(n) for n = 1..10000

44^PrimeOmega[Range[50]] (* Harvey P. Dale, Feb 22 2012 *)

a(n) = 44^bigomega(n); \\ Altug Alkan, Apr 16 2016

a(n) = A009988(A001222(n)) = 44^bigomega(n) = 44^A001222(n).

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A009966 Powers of 22.

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A218747 a(n) = (44^n - 1)/43.

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A165865 Totally multiplicative sequence with a(p) = 44.

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