This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A225231 Schur numbers S(3,n). 1
 9, 16, 23, 37, 53, 71, 93, 119, 147, 177, 211, 249, 289, 331, 377, 427, 479, 533, 591, 653, 717, 783, 853, 927, 1003, 1081, 1163, 1249, 1337, 1427, 1521, 1619, 1719, 1821, 1927, 2037, 2149, 2263, 2381, 2503, 2627, 2753, 2883, 3017, 3153, 3291, 3433 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 COMMENTS a(n) is, by definition, the least positive m such that if {1,...,m} is written as a disjoint union of sets A and B, then either A contains 3 distinct numbers, one the sum of the other two, or B contains n distinct numbers, one the sum of the other n - 1. LINKS Eric M. Schmidt, Table of n, a(n) for n = 3..1000 Tanbir Ahmed, Michael G. Eldredge, Jonathan J. Marler, and Hunter S. Snevily, Strict Schur Numbers, INTEGERS, Electronic J. of Combinatorial Number Theory, Vol. 13, Paper A22, 2013. Index entries for linear recurrences with constant coefficients, signature (3,-4,4,-3,1). FORMULA For n >= 5, a(n) = 3n^2/2 - 7n/2 + c, where c = 3 if n == 0,1 (mod 4), else c = 4. G.f.: x^3*(3*x^6-7*x^5+3*x^4+4*x^3-11*x^2+11*x-9) / ((x-1)^3*(x^2+1)). - Colin Barker, May 16 2013 MATHEMATICA Join[{9, 16}, LinearRecurrence[{3, -4, 4, -3, 1}, {23, 37, 53, 71, 93}, 45]] (* Ray Chandler, Feb 13 2014 *) PROG (Sage) def A225231(n) : return 9 if n == 3 else 16 if n == 4 else (3*n^2 - 7*n)//2 + [3, 3, 4, 4][n%4] CROSSREFS Cf. A030126, A045652, A072842. Sequence in context: A046463 A003332 A091571 * A151973 A102219 A227650 Adjacent sequences:  A225228 A225229 A225230 * A225232 A225233 A225234 KEYWORD nonn,easy AUTHOR Eric M. Schmidt, May 03 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.