A133999 a(1) = a(2) = 1; a(n+1) = round( a(n) + sqrt(3)*a(n-1) ).

1, 1, 3, 5, 10, 19, 36, 69, 131, 251, 478, 913, 1741, 3322, 6338, 12092, 23070, 44014, 83972, 160206, 305650, 583135, 1112536, 2122555, 4049524, 7725897, 14739878, 28121524, 53651742, 102359650, 195287193, 372579307, 710826647, 1356152937, 2587340805

Offset

1,3

Links

Bruno Berselli, Table of n, a(n) for n = 1..1000

Example

a(7) = 36 because a(6) is 19 and sqrt(3)*a(5) = 17.32, round(19+17.32) = 36

Mathematica

RecurrenceTable[{a[0] == a[1] == 1, a[n] == Floor[a[n - 1] + Sqrt[3] a[n - 2] + 1/2]}, a[n], {n, 0, 40}] (* Bruno Berselli, Mar 25 2014 *)
nxt[{a_, b_}]:={b, Round[b+a*Sqrt[3]]}; NestList[nxt, {1, 1}, 40][[All, 1]] (* Harvey P. Dale, Aug 27 2017 *)

Prog

(PARI) lista(nn) = {va = vector(nn); va[1] = 1; va[2] = 1; print1(va[1], ", ", va[2], ", "); for (n=3, nn, va[n] = round(va[n-1] + sqrt(3)*va[n-2]); print1(va[n], ", "); ); } \\ Michel Marcus, Mar 24 2014

Crossrefs

Sequence in context: A291735 A261050 A158943 * A238431 A014610 A117591

Adjacent sequences: A133996 A133997 A133998 * A134000 A134001 A134002

Keyword

nonn,easy

Author

Ben Paul Thurston, Jan 09 2008

Extensions

More terms from Michel Marcus, Mar 24 2014

Status

approved