A119565 a(0)=1, a(1)=2, a(2)=3, a(3)=5, a(4)=7, a(5)=10; a(n) = floor(a(n-1) + 1 + a(n-2)/6) for n>=6.

1, 2, 3, 5, 7, 10, 12, 14, 17, 20, 23, 27, 31, 36, 42, 49, 57, 66, 76, 88, 101, 116, 133, 153, 176, 202, 232, 266, 305, 350, 401, 460, 527, 604, 692, 793, 909, 1042, 1194, 1368, 1568, 1797, 2059, 2359, 2703, 3097, 3548, 4065, 4657, 5335, 6112, 7002, 8021

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Maple

for i from 0 to 5 do A[i]:= [1, 2, 3, 5, 7, 10][i+1] od:
for i from 6 to 100 do A[i]:= floor(A[i-1]+1+A[i-2]/6) od:
convert(A, list); # Robert Israel, Dec 08 2024

Mathematica

a[0]=1; a[1]=2; a[2]=3; a[3]=5; a[4]=7; a[5]=10; a[n_]:=a[n]=Floor[a[n-1]+1+a[n-2]/6];
Join[{1, 2, 3, 5}, RecurrenceTable[{a[4]==7, a[5]==10, a[n]==Floor[a[n-1]+ 1+ a[n-2]/6]}, a, {n, 60}]] (* Harvey P. Dale, Mar 15 2016 *)
nxt[{a_, b_}]:={b, Floor[b+1+a/6]}; Join[{1, 2, 3, 5}, NestList[nxt, {7, 10}, 50][[;; , 1]]] (* Harvey P. Dale, Jul 08 2023 *)

Prog

(PARI) a=concat([1, 2, 3, 5, 7, 10], vector(95)); for(i=7, #a, a[i]=1+a[i-1]+a[i-2]\6); a \\ Charles R Greathouse IV, Nov 07 2011

Crossrefs

Cf. A119592.

Sequence in context: A144726 A123885 A010062 * A119592 A191892 A087539

Adjacent sequences: A119562 A119563 A119564 * A119566 A119567 A119568

Keyword

nonn

Author

Roger L. Bagula, May 31 2006

Extensions

More terms from Zak Seidov, May 31 2006

Edited by N. J. A. Sloane, Jun 03 2006

Status

approved