OFFSET
0,3
COMMENTS
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
James Propp, Problem 1047, Math. Mag., 52 (1979), 265.
Jeffrey Shallit, Letter to N. J. A. Sloane, Nov 10 1979. Attached: James Propp, Problem 1047, Math. Mag., 52 (1979), 265. [Annotated scanned copy]
Aaron Snook, Augmented Integer Linear Recurrences, Thesis, 2012. - From N. J. A. Sloane, Dec 19 2012
FORMULA
For any k in {0, 1, 2, ...} and r in {0, 1, 2}, we have: if n = 6*k + (3/2)*k*(k-1) + r*(k+2), then a(n) = 3*k + r + 1. E.g., for k=3 and r=1, we have n = 6*3 + (3/2)*3*(3-1) + 1*(3+2) = 32 and so a(32) = 3*3 + 1 + 1 = 11. - Francois Jooste (phukraut(AT)hotmail.com), Mar 12 2002
MATHEMATICA
Table[n+1, {n, 0, 20}, {Ceiling[(n+1)/3]+1}] // Flatten (* Jean-François Alcover, Dec 10 2014 *)
PROG
(Haskell)
a005041 n = a005041_list !! n
a005041_list = 1 : f 1 1 (tail ts) where
f y i gs'@((j, a):gs) | i < j = y : f y (i+1) gs'
| i == j = a : f a (i+1) gs
ts = [(6*k + 3*k*(k-1) `div` 2 + r*(k+2), 3*k+r+1) |
k <- [0..], r <- [0, 1, 2]]
-- Reinhard Zumkeller, Mar 16 2012
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
EXTENSIONS
More terms from Samuel Hilliard (sam_spade1977(AT)hotmail.com), Apr 11 2004
STATUS
approved