A061583 -id:A061583 - cp's OEIS frontend

A038718 Number of permutations P of {1,2,...,n} such that P(1)=1 and |P^-1(i+1)-P^-1(i)| equals 1 or 2 for i=1,2,...,n-1.

1, 1, 2, 4, 6, 9, 14, 21, 31, 46, 68, 100, 147, 216, 317, 465, 682, 1000, 1466, 2149, 3150, 4617, 6767, 9918, 14536, 21304, 31223, 45760, 67065, 98289, 144050, 211116, 309406, 453457, 664574, 973981, 1427439, 2092014, 3065996, 4493436, 6585451

Offset: 1

John W. Layman, May 02 2000

This sequence is the number of digits of each term of A061583. - Dmitry Kamenetsky, Jan 17 2009

Michael De Vlieger, Table of n, a(n) for n = 1..6023
Dominika Závacká, Cristina Dalfó, and Miquel Angel Fiol, Integer sequences from k-iterated line digraphs, CEUR: Proc. 24th Conf. Info. Tech. - Appl. and Theory (ITAT 2024) Vol 3792, 156-161. See p. 161, Table 2.
Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-1).

Cf. A003274, A003410.

LinearRecurrence[{2,-1,1,-1},{1,1,2,4},50] (* or *) CoefficientList[ Series[(x^2-x+1)/(x^4-x^3+x^2-2x+1),{x,0,50}],x] (* Harvey P. Dale, Apr 24 2011 *)

a(n)=([0,1,0,0; 0,0,1,0; 0,0,0,1; -1,1,-1,2]^(n-1)*[1;1;2;4])[1,1] \\ Charles R Greathouse IV, Apr 07 2016

From Joseph Myers, Feb 03 2004: (Start)
G.f.: (1 -x +x^2)/(1-2*x+x^2-x^3+x^4).
a(n) = a(n-1) + a(n-3) + 1. (End)
a(n) = Sum_{i=1..n} A058278(i) = A097333(n) - 1. - R. J. Mathar, Oct 16 2010

More terms from Joseph Myers, Feb 03 2004

A061584 a(1) = 1, a(n)= number obtained by replacing each digit of a(n-1) with six times its value.

Original entry on oeis.org

1, 6, 36, 1836, 6481836, 3624486481836, 1836122424483624486481836, 64818366121224122424481836122424483624486481836, 362448648183636612612122461212241224244864818366121224122424481836122424483624486481836

Offset: 1

Amarnath Murthy, May 13 2001

a(n) contains all of a(n-1) as its least significant digits.

John Cerkan, Table of n, a(n) for n = 1..13

Cf. A061581, A061582, A061583, A061585, A061586, A061587, A061533.

NestList[FromDigits[Flatten[IntegerDigits/@(6 IntegerDigits[#])]]&,1,10] (* Harvey P. Dale, Aug 26 2022 *)

def A061584_first(n):
    an = "1"
    a061584 = []
    while n > 1:
        a061584.append(int(an))
        newan = ""
        for i in an:
            newan += str(6*int(i))
        an = newan
        n -= 1
    a061584.append(int(an))
    return a061584 # John Cerkan, May 25 2018

More terms from Larry Reeves (larryr(AT)acm.org) and Asher Auel, May 15 2001

A061585 a(1) = 1, a(n)= number obtained by replacing each digit of a(n-1) with seven times its value.

Original entry on oeis.org

1, 7, 49, 2863, 14564221, 72835422814147, 49145621352814145672872849, 286372835421472135145672872835424914564914562863, 1456422149145621352814728491472135728354249145649145621352814286372835422863728354214564221

Offset: 1

Amarnath Murthy, May 13 2001

John Cerkan, Table of n, a(n) for n = 1..12

Cf. A061581, A061582, A061583, A061584, A061586, A061587.

NestList[FromDigits[Flatten[IntegerDigits/@(7*IntegerDigits[#])]]&,1,10] (* Harvey P. Dale, Jan 23 2015 *)

A061585(n=2,a=1,m=7)={while(n--,a=eval(concat(apply(t->Str(t),digits(a)*m))));a} \\ If only the 2nd argument is given, then the operation is applied once to that argument. - M. F. Hasler, Jun 24 2016

def A061585_first(n):
    an = "1"
    a061585 = []
    while n > 1:
        a061585.append(int(an))
        newan = ""
        for i in an:
            newan += str(7*int(i))
        an = newan
        n -= 1
    a061585.append(int(an))
    return a061585 # John Cerkan, May 25 2018

More terms from Larry Reeves (larryr(AT)acm.org) and Asher Auel, May 15 2001

Corrected by Harvey P. Dale, Jan 23 2015

A061580 a(1) = 1, a(n)= number obtained by replacing each digit of a(n-1) with four times its value.

Original entry on oeis.org

1, 4, 16, 424, 16816, 42432424, 1681612816816, 42432424483242432424, 168161281681616321281681612816816, 42432424483242432424424128483242432424483242432424

Offset: 1

Amarnath Murthy, May 13 2001

Michael De Vlieger, Table of n, a(n) for n = 1..16

Cf. A061581, A061582, A061583, A061584, A061585, A061586, A061587.

NestList[FromDigits@ Flatten@ Map[IntegerDigits, 4*IntegerDigits[#]] &, 1, 9] (* Michael De Vlieger, Feb 25 2023 *)

More terms from Larry Reeves (larryr(AT)acm.org) and Asher Auel, May 15 2001
a(9) corrected by N. J. A. Sloane, Jan 23 2017 at the suggestion of Carolyn Liao.
a(10) corrected by Sean A. Irvine, Feb 25 2023

cp's OEIS Frontend

A038718 Number of permutations P of {1,2,...,n} such that P(1)=1 and |P^-1(i+1)-P^-1(i)| equals 1 or 2 for i=1,2,...,n-1.

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A061584 a(1) = 1, a(n)= number obtained by replacing each digit of a(n-1) with six times its value.

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A061585 a(1) = 1, a(n)= number obtained by replacing each digit of a(n-1) with seven times its value.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Python

Extensions

A061580 a(1) = 1, a(n)= number obtained by replacing each digit of a(n-1) with four times its value.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions