A164539 -id:A164539 - cp's OEIS frontend

A164675 a(n) = 8*a(n-2) for n > 2; a(1) = 1, a(2) = 12.

1, 12, 8, 96, 64, 768, 512, 6144, 4096, 49152, 32768, 393216, 262144, 3145728, 2097152, 25165824, 16777216, 201326592, 134217728, 1610612736, 1073741824, 12884901888, 8589934592, 103079215104, 68719476736, 824633720832

Offset: 1

Klaus Brockhaus, Aug 20 2009

Interleaving of A001018 and 12*A001018.

Binomial transform is A164539.

Vincenzo Librandi, Table of n, a(n) for n = 1..500
Index entries for linear recurrences with constant coefficients, signature (0,8).

Cf. A001018 (powers of 8), A164539.

[ n le 2 select 11*n-10 else 8*Self(n-2): n in [1..26] ];

Riffle[#, 12*#] & [8^Range[0, 14]] (* or *)
LinearRecurrence[{0, 8}, {1, 12}, 30] (* Paolo Xausa, Apr 22 2024 *)

a(n) = (5+(-1)^n)*2^(1/4*(6*n-11+3*(-1)^n)).

G.f.: x*(1+12*x)/(1-8*x^2).

A164540 a(n) = 4a(n-1) + 4a(n-2) for n > 1; a(0) = 1, a(1) = 14.

Original entry on oeis.org

1, 14, 60, 296, 1424, 6880, 33216, 160384, 774400, 3739136, 18054144, 87173120, 420909056, 2032328704, 9812951040, 47381118976, 228776280064, 1104629596160, 5333623504896, 25753012404224, 124346543636480, 600398224162816

Offset: 0

Al Hakanson (hawkuu(AT)gmail.com), Aug 15 2009

Binomial transform of A164539. Second binomial transform of A164675. Inverse binomial transform of A164541.

Vincenzo Librandi, Table of n, a(n) for n = 0..164
Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.
Index entries for linear recurrences with constant coefficients, signature (4, 4).

Cf. A164539, A164675, A164541.

Z:=PolynomialRing(Integers()); N:=NumberField(x^2-2); S:=[ ((1+3*r)*(2+2*r)^n+(1-3*r)*(2-2*r)^n)/2: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 20 2009

LinearRecurrence[{4,4},{1,14},30] (* Harvey P. Dale, Jul 18 2024 *)

a(n) = 4*a(n-1) + 4*a(n-2) for n > 1; a(0) = 1, a(1) = 14.
G.f.: (1+10*x)/(1-4*x-4*x^2).
a(n) = ((1+3*sqrt(2))*(2+2*sqrt(2))^n + (1-3*sqrt(2))*(2-2*sqrt(2))^n)/2.

Edited and extended beyond a(5) by Klaus Brockhaus, Aug 20 2009

cp's OEIS Frontend

A164675 a(n) = 8*a(n-2) for n > 2; a(1) = 1, a(2) = 12.

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A164540 a(n) = 4a(n-1) + 4a(n-2) for n > 1; a(0) = 1, a(1) = 14.

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cp's OEIS Frontend

A164675 a(n) = 8*a(n-2) for n > 2; a(1) = 1, a(2) = 12.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

Formula

A164540 a(n) = 4*a(n-1) + 4*a(n-2) for n > 1; a(0) = 1, a(1) = 14.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

Formula

Extensions

A164540 a(n) = 4a(n-1) + 4a(n-2) for n > 1; a(0) = 1, a(1) = 14.