A228467 Recurrence a(n) = 2^n*a(n-1) - a(n-2) with a(0)=0, a(1)=1.

0, 1, 4, 31, 492, 15713, 1005140, 128642207, 32931399852, 16860748082017, 17265373104585556, 35359467257443136671, 144832360621113983218860, 1186466662848698493085764449, 19439069659280715489603181513556, 636979433408843822314618558750438559

Offset: 0

Author

Vaclav Kotesovec, Aug 22 2013

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..81

Crossrefs

Cf. A225609, A076131, A073587, A073588, A228465, A006116.

Programs

Mathematica

RecurrenceTable[{a[n]==2^n*a[n-1]-a[n-2],a[0]==0,a[1]==1},a,{n,0,15}]
nxt[{n_,a_,b_}]:={n+1,b,b*2^(n+1)-a}; NestList[nxt,{1,0,1},20][[All,2]] (* Harvey P. Dale, Jul 02 2022 *)

Formula

a(n) ~ c * 2^(n^2/2 + n/2), where c = 0.4792100640621967581293535977698228585...