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.

Showing 1-2 of 2 results.

A163146 a(n) = 12*a(n-1)-31*a(n-2) for n > 1; a(0) = 1, a(1) = 11.

Original entry on oeis.org

1, 11, 101, 871, 7321, 60851, 503261, 4152751, 34231921, 282047771, 2323383701, 19137123511, 157620587401, 1298196219971, 10692116430221, 88061314343551, 725280162785761, 5973461208779051, 49197849458990021, 405196896035729671
Offset: 0

Views

Author

Klaus Brockhaus, Jul 21 2009

Keywords

Comments

Binomial transform of A093145 without initial 0. Inverse binomial transform of A163147.

Links

Crossrefs

Cf. A093145, A163147.

Programs

  • Magma
    [ n le 2 select 10*n-9 else 12*Self(n-1)-31*Self(n-2): n in [1..20] ];
  • Mathematica
    LinearRecurrence[{12,-31},{1,11},20] (* Harvey P. Dale, Apr 15 2019 *)

Formula

a(n) = ((1+sqrt(5))*(6+sqrt(5))^n+(1-sqrt(5))*(6-sqrt(5))^n)/2.
G.f.: (1-x)/(1-12*x+31*x^2).

A163148 a(n) = 16*a(n-1) - 59*a(n-2) for n > 1; a(0) = 1, a(1) = 13.

Original entry on oeis.org

1, 13, 149, 1617, 17081, 177893, 1838509, 18920457, 194255281, 1991777533, 20407378949, 209003188737, 2140015661801, 21909062453333, 224284075207069, 2295910518566457, 23501807859846241, 240570205162118893
Offset: 0

Views

Author

Klaus Brockhaus, Jul 21 2009

Keywords

Comments

Binomial transform of A163147.

Links

Crossrefs

Cf. A163147.

Programs

  • Magma
    [ n le 2 select 12*n-11 else 16*Self(n-1)-59*Self(n-2): n in [1..18] ];
  • PARI
    Vec((1-3*x)/(1-16*x+59*x^2) + O(x^30)) \\ Jinyuan Wang, Mar 23 2020

Formula

a(n) = ((1+sqrt(5))*(8+sqrt(5))^n+(1-sqrt(5))*(8-sqrt(5))^n)/2.
G.f.: (1-3*x)/(1-16*x+59*x^2).
Showing 1-2 of 2 results.

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