A164110 -id:A164110 - cp's OEIS frontend

A164095 a(n) = 2*a(n-2) for n > 2; a(1) = 5, a(2) = 6.

5, 6, 10, 12, 20, 24, 40, 48, 80, 96, 160, 192, 320, 384, 640, 768, 1280, 1536, 2560, 3072, 5120, 6144, 10240, 12288, 20480, 24576, 40960, 49152, 81920, 98304, 163840, 196608, 327680, 393216, 655360, 786432, 1310720, 1572864, 2621440, 3145728

Offset: 1

Klaus Brockhaus, Aug 10 2009

nonn

Interleaving of A020714 and A007283 without initial term 3.
Partial sums are in A164096.
Binomial transform is A048655 without initial 1, second binomial transform is A161941 without initial 2, third binomial transform is A164037, fourth binomial transform is A161731 without initial 1, fifth binomial transform is A164038, sixth binomial transform is A164110.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0, 2).

Cf. A020714 (5*2^n), A007283 (3*2^n), A164096, A048655, A161941, A164037, A161731, A164038, A164110, A070876.

[ n le 2 select n+4 else 2*Self(n-2): n in [1..40] ];

LinearRecurrence[{0,2},{5,6},50] (* or *) With[{nn=20},Riffle[NestList[ 2#&,5,nn],NestList[2#&,6,nn]]] (* Harvey P. Dale, Aug 15 2020 *)

a(n) = A070876(n)/3.
a(n) = (4-(-1)^n)*2^(1/4*(2*n-1+(-1)^n)).
G.f.: x*(5+6*x)/(1-2*x^2).

A164038 Expansion of (5-19x)/(1-10x+23*x^2).

Original entry on oeis.org

5, 31, 195, 1237, 7885, 50399, 322635, 2067173, 13251125, 84966271, 544886835, 3494644117, 22414043965, 143763624959, 922113238395, 5914569009893, 37937085615845, 243335768930911, 1560804720144675, 10011324516035797

Offset: 0

Al Hakanson (hawkuu(AT)gmail.com), Aug 08 2009

Binomial transform of A161731 without initial 1. Fifth binomial transform of A164095. Inverse binomial transform of A164110.

G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..100 from Vincenzo Librandi)
Index entries for linear recurrences with constant coefficients, signature (10,-23).

Cf. A161731, A164095, A164110.

Z:= PolynomialRing(Integers()); N:=NumberField(x^2-2); S:=[ ((5+3*r)*(5+r)^n+(5-3*r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 10 2009

LinearRecurrence[{10,-23},{5,31},50] (* or *) CoefficientList[Series[(5 - 19*x)/(1 - 10*x + 23*x^2), {x,0,50}], x] (* G. C. Greubel, Sep 08 2017 *)

Vec((5-19*x)/(1-10*x+23*x^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 5, a(1) = 31.
G.f.: (5-19*x)/(1-10*x+23*x^2).
a(n) = ((5+3*sqrt(2))*(5+sqrt(2))^n + (5-3*sqrt(2))*(5-sqrt(2))^n)/2.
E.g.f: (5*cosh(sqrt(2)*x) + 3*sqrt(2)*sinh(sqrt(2)*x))*exp(5*x). - G. C. Greubel, Sep 08 2017

Edited and extended beyond a(5) by Klaus Brockhaus, Aug 10 2009

cp's OEIS Frontend

A164095 a(n) = 2*a(n-2) for n > 2; a(1) = 5, a(2) = 6.

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A164038 Expansion of (5-19x)/(1-10x+23*x^2).

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cp's OEIS Frontend

A164095 a(n) = 2*a(n-2) for n > 2; a(1) = 5, a(2) = 6.

Views

Author

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Magma

Mathematica

Formula

A164038 Expansion of (5-19*x)/(1-10*x+23*x^2).

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Magma

Mathematica

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Formula

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A164038 Expansion of (5-19x)/(1-10x+23*x^2).