A167032 -id:A167032 - cp's OEIS frontend

A166915 a(n) = 20a(n-1) - 64a(n-2) - 45 for n>1; a(0) = 399, a(1) = 5695.

399, 5695, 88319, 1401855, 22384639, 357974015, 5726863359, 91626930175, 1466019348479, 23456263438335, 375300030463999, 6004799749226495, 96076793034833919, 1537228676746182655, 24595658780694282239

Offset: 0

Klaus Brockhaus, Oct 27 2009

Related to Reverse and Add trajectory of 318 in base 4: A075153(6*n+3) = 15*a(n).

lim_{n -> infinity} a(n)/a(n-1) = 16.

G. C. Greubel, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (21, -84, 64).

Cf. A075153, A166912, A166913, A166914, A166916, A166917, A006105, A167031, A167032, A167033.

LinearRecurrence[{21, -84, 64}, {399, 5695, 88319}, 50] (* G. C. Greubel, May 28 2016 *)

m=15; v=concat([399, 5695], vector(m-2)); for(n=3, m, v[n]=20*v[n-1]-64*v[n-2]-45); v

a(n) = (1024*16^n + 176*4^n - 3)/3.
G.f.: (399 - 2684*x + 2240*x^2)/((1-x)*(1-4*x)*(1-16*x)).
From G. C. Greubel, May 28 2016: (Start)
a(n) = 21*a(n-1) - 84*a(n-2) + 64*a(n-3).
E.g.f.: (1/3)*(1024*exp(16*x) + 176*exp(4*x) - 3*exp(x)). (End)

A166916 a(n) = 20a(n-1) - 64a(n-2) - 15 for n > 1; a(0) = 357, a(1) = 5525.

Original entry on oeis.org

357, 5525, 87637, 1399125, 22373717, 357930325, 5726688597, 91626231125, 1466016552277, 23456252253525, 375299985724757, 6004799570269525, 96076792319006037, 1537228673882871125, 24595658769241036117

Offset: 0

Klaus Brockhaus, Oct 27 2009

Related to Reverse and Add trajectory of 318 in base 4: A075153(6*n+4) = 30*a(n).

lim_{n -> infinity} a(n)/a(n-1) = 16.

G. C. Greubel, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (21, -84, 64).

Cf. A075153, A166912, A166913, A166914, A166915, A166917, A006105, A167031, A167032, A167033.

LinearRecurrence[{21,-84,64},{357,5525,87637},20] (* Harvey P. Dale, Sep 24 2012 *)

m=15; v=concat([357, 5525], vector(m-2)); for(n=3, m, v[n]=20*v[n-1]-64*v[n-2]-15); v

a(n) = (1024*16^n + 48*4^n - 1)/3.
G.f.: (357 - 1972*x + 1600*x^2)/((1-x)*(1-4*x)*(1-16*x)).
a(0)=357, a(1)=5525, a(2)=87637, a(n)=21*a(n-1)-84*a(n-2)+64*a(n-3). - Harvey P. Dale, Sep 24 2012
E.g.f.: (1/3)*(1024*exp(16*x) + 48*exp(4*x) - exp(x)). - G. C. Greubel, May 28 2016

A167031 a(n) = 20a(n-1) - 64a(n-2) + 1 for n > 1; a(0) = 1, a(1) = 20.

Original entry on oeis.org

1, 20, 337, 5461, 87653, 1403557, 22461349, 359399333, 5750460325, 92007649189, 1472123522981, 23553980911525, 376863712759717, 6029819476856741, 96477111920512933, 1543633791891427237, 24698140674915717029

Offset: 0

Klaus Brockhaus, Oct 27 2009

nonn

lim_{n -> infinity} a(n)/a(n-1) = 16.

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (21,-84,64).

Cf. A166915, A166916, A006105, A167032, A167033.

[ n le 2 select 19*n-18 else 20*Self(n-1)-64*Self(n-2)+1: n in [1..17] ];

LinearRecurrence[{21, -84, 64}, {1, 20, 337}, 50] (* G. C. Greubel, May 30 2016 *)

a(n) = (241*16^n - 65*4^n + 4)/180.
G.f.: (1-x+x^2)/((1-x)*(1-4*x)*(1-16*x)).
From G. C. Greubel, May 30 2016: (Start)
a(n) = 21*a(n-1) - 84*a(n-2) + 64*a(n-2).
E.g.f.: (1/180)*(241*exp(16*x) - 65*exp(4*x) + 4*exp(x)). (End)

A167033 a(n) = 20a(n-1) - 64a(n-2) + 3 for n > 1; a(0) = 1, a(1) = 22.

Original entry on oeis.org

1, 22, 379, 6175, 99247, 1589743, 25443055, 407117551, 6513995503, 104224386799, 1667592023791, 26681479720687, 426903704891119, 6830459395698415, 109287350800936687, 1748597614694035183, 27977561842620755695

Offset: 0

Klaus Brockhaus, Oct 27 2009

nonn

lim_{n -> infinity} a(n)/a(n-1) = 16.

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (21,-84,64).

Cf. A166915, A166916, A006105, A167031, A167032.

[ n le 2 select 21*n-20 else 20*Self(n-1)-64*Self(n-2)+3: n in [1..17] ];

LinearRecurrence[{21, -84, 64}, {1, 22, 379}, 50] (* G. C. Greubel, May 30 2016 *)

a(n) = (91*16^n - 35*4^n + 4)/60.
G.f.: (1+x+x^2)/((1-x)*(1-4*x)*(1-16*x)).
From G. C. Greubel, May 30 2016: (Start)
a(n) = 21*a(n-1) - 84*a(n-2) + 64*a(n-3).
E.g.f.: (1/60)*(91*exp(16*x) - 35*exp(4*x) + 4*exp(x)). (End)

cp's OEIS Frontend

A166915 a(n) = 20*a(n-1) - 64*a(n-2) - 45 for n>1; a(0) = 399, a(1) = 5695.

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A166916 a(n) = 20*a(n-1) - 64*a(n-2) - 15 for n > 1; a(0) = 357, a(1) = 5525.

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A167031 a(n) = 20*a(n-1) - 64*a(n-2) + 1 for n > 1; a(0) = 1, a(1) = 20.

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A167033 a(n) = 20*a(n-1) - 64*a(n-2) + 3 for n > 1; a(0) = 1, a(1) = 22.

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Author

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Magma

Mathematica

Formula

A166915 a(n) = 20a(n-1) - 64a(n-2) - 45 for n>1; a(0) = 399, a(1) = 5695.

A166916 a(n) = 20a(n-1) - 64a(n-2) - 15 for n > 1; a(0) = 357, a(1) = 5525.

A167031 a(n) = 20a(n-1) - 64a(n-2) + 1 for n > 1; a(0) = 1, a(1) = 20.

A167033 a(n) = 20a(n-1) - 64a(n-2) + 3 for n > 1; a(0) = 1, a(1) = 22.