A152266 -id:A152266 - cp's OEIS frontend

A152265 a(n) = ((8 + sqrt(7))^n + (8 - sqrt(7))^n)/2.

1, 8, 71, 680, 6833, 70568, 739607, 7811336, 82823777, 879934280, 9357993191, 99571637096, 1059740581649, 11280265991912, 120079042716599, 1278289521926600, 13608126915979457, 144867527905855112

Offset: 0

Al Hakanson (hawkuu(AT)gmail.com), Dec 01 2008

nonn

Binomial transform of A145302. Inverse binomial transform of A152266. - Philippe Deléham, Dec 03 2008

Index entries for linear recurrences with constant coefficients, signature (16, -57).

Cf. A056241, A098158, A145302, A152266.

Z:= PolynomialRing(Integers()); N:=NumberField(x^2-7); S:=[ ((8+r7)^n+(8-r7)^n)/2: n in [0..17] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Dec 03 2008

From Philippe Deléham, Dec 03 2008: (Start)
a(n) = 16*a(n-1) - 57*a(n-2), n > 1; a(0)=1, a(1)=8.
G.f.: (1-8*x)/(1-16*x+57*x^2).
a(n) = Sum_{k=0..n} A098158(n,k)*8^(2k-n)*7^(n-k). (End)
a(n) = Sum_{k=1..n} A056241(n,k) * 7^(k-1). - J. Conrad, Nov 23 2022

Extended beyond a(6) by Klaus Brockhaus, Dec 03 2008

A163192 a(n) = 20a(n-1)-93a(n-2) for n > 1; a(0) = 1, a(1) = 10.

Original entry on oeis.org

1, 10, 107, 1210, 14249, 172450, 2123843, 26439010, 331262801, 4166428090, 52521121307, 662944613770, 8374427993849, 105834710796370, 1337872412499443, 16914820145926450, 213874268556080801

Offset: 0

Klaus Brockhaus, Jul 22 2009

nonn

Binomial transform of A152266. Tenth binomial transform of powers of 7 interleaved with zeros.

Harvey P. Dale, Table of n, a(n) for n = 0..900
Index entries for linear recurrences with constant coefficients, signature (20, -93).

Cf. A152266, A000420 (powers of 7).

[ n le 2 select 9*n-8 else 20*Self(n-1)-93*Self(n-2): n in [1..17] ];

LinearRecurrence[{20,-93},{1,10},40] (* Harvey P. Dale, Nov 01 2011 *)

a(n) = ((10+sqrt(7))^n+(10-sqrt(7))^n)/2.

G.f.: (1-10*x)/(1-20*x+93*x^2).

cp's OEIS Frontend

A152265 a(n) = ((8 + sqrt(7))^n + (8 - sqrt(7))^n)/2.

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A163192 a(n) = 20a(n-1)-93a(n-2) for n > 1; a(0) = 1, a(1) = 10.

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cp's OEIS Frontend

A152265 a(n) = ((8 + sqrt(7))^n + (8 - sqrt(7))^n)/2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Formula

Extensions

A163192 a(n) = 20*a(n-1)-93*a(n-2) for n > 1; a(0) = 1, a(1) = 10.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

Formula

A163192 a(n) = 20a(n-1)-93a(n-2) for n > 1; a(0) = 1, a(1) = 10.