A022030 For even n, a(n+2) is the greatest integer such that a(n+2)/a(n+1) < a(n+1)/a(n); for odd n, the least integer such that a(n+2)/a(n+1) > a(n+1)/a(n); a(0) = 4, a(1) = 16.

4, 16, 63, 249, 984, 3889, 15370, 60745, 240075, 948819, 3749901, 14820274, 58572352, 231488326, 914882931, 3615779646, 14290202610, 56477415835, 223208766625, 882160643536, 3486455360919, 13779090092886, 54457408494633, 215225339261149, 850608722312629, 3361756570848769

Offset

0,1

Comments

Original definition: a(n+2) is the greatest integer such that a(n+2)/a(n+1) < a(n+1)/a(n).

This original definition would lead to sequence 4, 16, 63, 248, 976, 3841, ... which agrees to over 2000 terms with the conjectured g.f. = (4 - x^2)/(1 - 4*x + x^3). - M. F. Hasler, Feb 11 2016

Links

Table of n, a(n) for n=0..25.

Index entries for Pisot sequences

Formula

Conjecture: a(n) = 4*a(n-1)-a(n-3)+a(n-4). G.f. = (4-x^2+x^3)/(1-4*x+x^3-x^4). - Colin Barker, Feb 16 2012

a(n) = ceiling(a(n-1)^2/a(n-2))-1 for even n > 0, a(n) = floor(a(n-1)^2/a(n-2))+1 for even n > 0. - M. F. Hasler, Feb 11 2016

Prog

(PARI) a=[4, 16]; for(n=2, 2000, a=concat(a, if(bittest(n, 0), a[n]^2\a[n-1]+1, ceil(a[n]^2/a[n-1])-1))); A022030(n)=a[n+1] \\ M. F. Hasler, Feb 11 2016

Crossrefs

Cf. A022026 - A022032, A022018 - A022025.

Sequence in context: A099503 A119376 A282310 * A135450 A265032 A162547

Adjacent sequences: A022027 A022028 A022029 * A022031 A022032 A022033

Keyword

nonn

Author

R. K. Guy

Extensions

Edited (definition changed to fit data, extended to 3 lines) by M. F. Hasler, Feb 11 2016

Status

approved