A014007 Pisot sequence E(10,21), a(n) = floor( a(n-1)^2/a(n-2)+1/2 ).

10, 21, 44, 92, 192, 401, 838, 1751, 3659, 7646, 15977, 33385, 69760, 145768, 304592, 636465, 1329935, 2778986, 5806873, 12133841, 25354455, 52979793, 110704745, 231324810, 483368330, 1010029761, 2110523290, 4410076544, 9215143569, 19255645599, 40235931720

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..1000

D. W. Boyd, Some integer sequences related to the Pisot sequences, Acta Arithmetica, 34 (1979), 295-305.

D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993.

Formula

Known not to satisfy any linear recurrence.

Prog

(PARI) pisotE(nmax, a1, a2) = {
  a=vector(nmax); a[1]=a1; a[2]=a2;
  for(n=3, nmax, a[n] = floor(a[n-1]^2/a[n-2]+1/2));
  a
}
pisotE(50, 10, 21) \\ Colin Barker, Jul 29 2016

Crossrefs

Sequence in context: A095824 A086225 A240994 * A074254 A122963 A067520

Adjacent sequences: A014004 A014005 A014006 * A014008 A014009 A014010

Keyword

nonn

Author

Simon Plouffe

Status

approved