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

0,3

Links

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

Formula

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

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 *)

Crossrefs

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

Sequence in context: A350608 A143077 A203011 * A005841 A005828 A084764

Adjacent sequences: A228464 A228465 A228466 * A228468 A228469 A228470

Keyword

nonn

Author

Vaclav Kotesovec, Aug 22 2013

Status

approved