A001027 -id:A001027 - cp's OEIS frontend

A067416 Ninth column of triangle A067410.

1, 10, 180, 3240, 58320, 1049760, 18895680, 340122240, 6122200320, 110199605760, 1983592903680, 35704672266240, 642684100792320, 11568313814261760, 208229648656711680, 3748133675820810240

Offset: 0

Wolfdieter Lang, Jan 25 2002

Index entries for linear recurrences with constant coefficients, signature (18).

Cf. A067415 (eighth column), A001027 (powers of 18).

a(n)= A067410(n+8, 8). a(n)= 10*18^(n-1), n>=1, a(0)=1.

G.f. (1-8*x)/(1-18*x).

A197352 a(0)=0, a(1)=1, a(2n)=18*a(n), a(2n+1)=a(2n)+1.

Original entry on oeis.org

0, 1, 18, 19, 324, 325, 342, 343, 5832, 5833, 5850, 5851, 6156, 6157, 6174, 6175, 104976, 104977, 104994, 104995, 105300, 105301, 105318, 105319, 110808, 110809, 110826, 110827, 111132, 111133, 111150, 111151, 1889568, 1889569, 1889586, 1889587

Offset: 0

Philippe Deléham, Oct 14 2011

Numbers whose set of base 18 digits is {0,1}.

Sums of distinct powers of 18.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Identities and periodic oscillations of divide-and-conquer recurrences splitting at half, arXiv:2210.10968 [cs.DS], 2022, p. 45.

Cf. A001027, A104257, A197351.

[n: n in [0..2000000] | Set(IntegerToSequence(n, 18)) subset {0, 1}]; // Vincenzo Librandi, Jun 05 2012

FromDigits[#,18]&/@Tuples[{0,1},5] (* Vincenzo Librandi, Jun 05 2012 *)

a(n) = Sum_{k>=0} A030308(n,k)*18^k.

G.f.: (1/(1 - x))*Sum_{k>=0} 18^k*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jun 04 2017

A013886 a(n) = 18^(5*n + 1).

Original entry on oeis.org

18, 34012224, 64268410079232, 121439531096594251776, 229468251895129407139872768, 433595865796975883590475106484224, 819308872942260126404286866009182175232, 1548139828427760582529495524831238344488779776, 2925315479322586708409093799864313376118974623776768

Offset: 0

N. J. A. Sloane

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..50
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (1889568).

Cf. A001027.

[18^(5*n+1): n in [0..10]]; // Vincenzo Librandi, May 27 2011

18^(5*Range[0,20]+1) (* or *) NestList[1889568#&,18,10] (* Harvey P. Dale, Oct 29 2016 *)

a(n) = 18^(5*n+1); \\ Seiichi Manyama, Aug 15 2023

a(n) = 1889568*a(n-1), a(0)=18. - Vincenzo Librandi, May 27 2011

A013887 a(n) = 18^(5*n + 2).

Original entry on oeis.org

324, 612220032, 1156831381426176, 2185911559738696531968, 4130428534112329328517709824, 7804725584345565904628551916716032, 14747559712960682275277163588165279154176, 27866516911699690485530919446962290200798035968

Offset: 0

N. J. A. Sloane

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..50
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (1889568).

Cf. A001027.

[18^(5*n+2): n in [0..10]]; // Vincenzo Librandi, May 27 2011

a(n) = 1889568*a(n-1), a(0)=324. - Vincenzo Librandi, May 27 2011

A013888 a(n) = 18^(5*n + 3).

Original entry on oeis.org

5832, 11019960576, 20822964865671168, 39346408075296537575424, 74347713614021927913318776832, 140485060518220186283313934500888576, 265456074833292280954988944586975024775168, 501597304410594428739556550045321223614364647424

Offset: 0

N. J. A. Sloane

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..50
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (1889568).

Cf. A001027.

[18^(5*n+3): n in [0..10]]; // Vincenzo Librandi, May 27 2011

18^(5Range[0,20]+3) (* or *) NestList[1889568#&,5832,20] (* Harvey P. Dale, Jan 27 2023 *)

a(n) = 1889568*a(n-1), a(0)=5832. - Vincenzo Librandi, May 27 2011

A013889 a(n) = 18^(5*n + 4).

Original entry on oeis.org

104976, 198359290368, 374813367582081024, 708235345355337676357632, 1338258845052394702439737982976, 2528731089327963353099650821015994368, 4778209346999261057189801002565550445953024, 9028751479390699717312017900815782025058563653632

Offset: 0

N. J. A. Sloane

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..50
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (1889568).

Cf. A001027.

[18^(5*n+4): n in [0..10]]; // Vincenzo Librandi, May 27 2011

a(n) = 1889568*a(n-1), a(0)=104976. - Vincenzo Librandi, May 27 2011

A017958 Powers of sqrt(18) rounded down.

Original entry on oeis.org

1, 4, 18, 76, 324, 1374, 5832, 24743, 104976, 445375, 1889568, 8016758, 34012224, 144301645, 612220032, 2597429617, 11019960576, 46753733110, 198359290368, 841567195983, 3570467226624, 15148209527700

Offset: 0

N. J. A. Sloane

			sqrt(18)^2 = 18, so a(2) = 18.
sqrt(18)^3 = 76.3675323681471326352911911..., so a(3) = 76.
sqrt(18)^4 = 18^2 = 324, so a(4) = 324.
sqrt(18)^5 = 1374.61558262664838743524143993..., so a(5) = 1374.

Vincenzo Librandi, Table of n, a(n) for n = 0..800

Cf. A001027 (bisection)

[Floor(Sqrt(18^n)): n in [0..30]]; // Vincenzo Librandi, Jun 24 2011

Floor[Sqrt[18]^Range[0, 35]] (* Alonso del Arte, Dec 07 2017 *)

a(n)=sqrtint(18^n) \\ Charles R Greathouse IV, Nov 18 2011

a(n) = floor(sqrt(18^n)). - Vincenzo Librandi, Jun 24 2011

A017959 Powers of sqrt(18) rounded to nearest integer.

Original entry on oeis.org

1, 4, 18, 76, 324, 1375, 5832, 24743, 104976, 445375, 1889568, 8016758, 34012224, 144301645, 612220032, 2597429617, 11019960576, 46753733110, 198359290368, 841567195983, 3570467226624, 15148209527701

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Cf. A010474, A001027 (bisection).

[Round(Sqrt(18)^n): n in [0..30]]; // Vincenzo Librandi, Nov 20 2011

Digits:=1500: A017959:=n->round(sqrt(18)^n): seq(A017959(n), n=0..30); # Wesley Ivan Hurt, Apr 18 2017

Floor[(Sqrt[18])^Range[0,25]+1/2] (* Vincenzo Librandi, Nov 20 2011 *)

a(n)=round(sqrt(18)^n) \\ Charles R Greathouse IV, Nov 18 2011

A165839 Totally multiplicative sequence with a(p) = 18.

Original entry on oeis.org

1, 18, 18, 324, 18, 324, 18, 5832, 324, 324, 18, 5832, 18, 324, 324, 104976, 18, 5832, 18, 5832, 324, 324, 18, 104976, 324, 324, 5832, 5832, 18, 5832, 18, 1889568, 324, 324, 324, 104976, 18, 324, 324, 104976, 18, 5832, 18, 5832, 5832, 324, 18, 1889568, 324

Offset: 1

Jaroslav Krizek, Sep 28 2009

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

18^PrimeOmega[Range[100]] (* G. C. Greubel, Apr 09 2016 *)

a(n) = A001027(A001222(n)) = 18^bigomega(n) = 18^A001222(n).

A373818 Expansion of 1/(2 - 1/(1 - 9*x)^(1/3)).

Original entry on oeis.org

1, 3, 27, 261, 2592, 26082, 264384, 2691954, 27488403, 281236779, 2881239093, 29546332821, 303201787140, 3113043334560, 31974807932820, 328518361498968, 3376062893960244, 34700713221307482, 356719230542209212, 3667432457788644762, 37708163269636391982

Offset: 0

Seiichi Manyama, Aug 04 2024

Cf. A001027, A373939.

my(N=30, x='x+O('x^N)); Vec(1/(2-1/(1-9*x)^(1/3)))

a(n) = 9^n * Sum_{k>=0} (1/2)^(k+1) * binomial(n-1+k/3,n).

cp's OEIS Frontend

A067416 Ninth column of triangle A067410.

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A197352 a(0)=0, a(1)=1, a(2n)=18*a(n), a(2n+1)=a(2n)+1.

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A013886 a(n) = 18^(5*n + 1).

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A013887 a(n) = 18^(5*n + 2).

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A013888 a(n) = 18^(5*n + 3).

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A013889 a(n) = 18^(5*n + 4).

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A017958 Powers of sqrt(18) rounded down.

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A017959 Powers of sqrt(18) rounded to nearest integer.

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