The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A250353 Number of length 4 arrays x(i), i=1..4 with x(i) in i..i+n and no value appearing more than 2 times. 2
 16, 75, 235, 581, 1221, 2287, 3935, 6345, 9721, 14291, 20307, 28045, 37805, 49911, 64711, 82577, 103905, 129115, 158651, 192981, 232597, 278015, 329775, 388441, 454601, 528867, 611875, 704285, 806781, 920071, 1044887, 1181985, 1332145 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS There are n+1 candidates for any of the 4 values in the 4-tuple. If there were no constraints, there were (n+1)^4 arrays. The constraint of not counting the quadruplets (4,4,4,4), (5,5,5,5), ..... (n+1,n+1,n+1,n+1) discards n-2 of the 4-tuples. [The case n=1 is special because there are not quadruplets]. Adding the constraint of not having triplets discards (3,3,3,*) and (*,n+2,n+2,n+2) where the star represents one of n+1 values; this is a total of 2*(n+1). The constraint of not having triplets also discards the (*,4,4,4), (4,*,4,4), (4,4,*,4), (4,4,4,*), (*,5,5,5),... (*,1+n,1+n,1+n),....(1+n,1+n,1+n,*) where the star represents one of n values (not n+1 here not to account for the quadruplets twice). There are binomial(4,1)*n*(n-2) of these triplets. The result is a(n) = (n+1)^4 -(n-2) -2*(n+1) -4*n*(n-2) = n^4+4*n^3+2*n^2+9*n+1. - R. J. Mathar, Oct 11 2020 LINKS R. H. Hardin, Table of n, a(n) for n = 1..210 FORMULA a(n) = n^4 + 4*n^3 + 2*n^2 + 9*n + 1 for n>1. From Colin Barker, Nov 13 2018: (Start) G.f.: x*(16 - 5*x + 20*x^2 - 4*x^3 - 4*x^4 + x^5) / (1 - x)^5. a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>6. (End) EXAMPLE Some solutions for n=6: ..2....0....2....3....3....3....2....4....4....4....1....0....2....5....5....5 ..6....2....7....1....7....4....2....4....3....4....4....6....1....3....1....4 ..2....4....3....5....6....7....7....6....8....2....7....2....6....6....2....5 ..3....7....7....8....6....4....6....7....8....7....8....6....9....4....5....3 CROSSREFS Row 4 of A250351. Sequence in context: A197873 A232863 A200786 * A212690 A244835 A189949 Adjacent sequences: A250350 A250351 A250352 * A250354 A250355 A250356 KEYWORD nonn,easy AUTHOR R. H. Hardin, Nov 19 2014 STATUS approved

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

Last modified December 8 23:37 EST 2023. Contains 367681 sequences. (Running on oeis4.)