cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A145303 a(n) = ((8 + sqrt(8))^n + (8 - sqrt(8))^n)/2.

Original entry on oeis.org

1, 8, 72, 704, 7232, 76288, 815616, 8777728, 94769152, 1024753664, 11088986112, 120037572608, 1299617939456, 14071782965248, 152369922834432, 1649898919297024, 17865667030024192, 193456332999753728
Offset: 0

Views

Author

Al Hakanson (hawkuu(AT)gmail.com), Oct 06 2008

Keywords

Comments

Binomial transform is A152267, inverse binomial transform is A147689.

Links

Crossrefs

Cf. A081180, A098158, A152267, A147689.

Programs

  • Magma
    Z:= PolynomialRing(Integers()); N:=NumberField(x^2-8); S:=[ ((8+r8)^n+(8-r8)^n)/2: n in [0..17] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Oct 20 2008

Formula

From R. J. Mathar, Oct 10 2008: (Start)
a(n) = 16*a(n-1) - 56*a(n-2).
G.f.: (1-8x)/(1-16x+56x^2).
a(n) = 2^n*A081180(n+1) - 2^(n+2)*A081180(n). (End)
a(n) = Sum_{k=0..n} 8^k*A098158(n,k). - Philippe Deléham, Oct 14 2008

Extensions

More terms from R. J. Mathar, Oct 10 2008
Edited by Klaus Brockhaus, Jul 09 2009

A163206 a(n) = 20*a(n-1) - 92*a(n-2) for n > 1; a(0) = 1, a(1) = 10.

Original entry on oeis.org

1, 10, 108, 1240, 14864, 183200, 2296512, 29075840, 370237696, 4729776640, 60533664768, 775533844480, 9941579730944, 127482480926720, 1635024283287552, 20972097420492800, 269019714347401216, 3450961324262686720, 44269412765292822528, 567899813473689272320
Offset: 0

Views

Author

Klaus Brockhaus, Jul 28 2009

Keywords

Comments

Binomial transform of A152267. Tenth binomial transform of powers of 8 interleaved with zeros.

Links

Crossrefs

Cf. A152267, A001018 (powers of 8).

Programs

  • Magma
    [ n le 2 select 9*n-8 else 20*Self(n-1)-92*Self(n-2): n in [1..17] ];
  • Mathematica
    LinearRecurrence[{20, -92}, {1, 10}, 50] (* or *) Table[((10+Sqrt[8])^n + (10-Sqrt[8])^n)/2,{n,0,25}] (* G. C. Greubel, Dec 10 2016 *)
  • PARI
    Vec((1-10*x)/(1-20*x+92*x^2) + O(x^50)) \\ G. C. Greubel, Dec 10 2016

Formula

a(n) = ((10+sqrt(8))^n + (10-sqrt(8))^n)/2.
G.f.: (1-10*x)/(1-20*x+92*x^2).

Extensions

Terms a(18) - a(20) added by G. C. Greubel, Dec 10 2016
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