The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A241619 T(n,k)=Number of length n+2 0..k arrays with no consecutive three elements summing to more than k 15
 4, 10, 6, 20, 20, 9, 35, 50, 40, 13, 56, 105, 125, 76, 19, 84, 196, 315, 295, 147, 28, 120, 336, 686, 889, 711, 287, 41, 165, 540, 1344, 2254, 2567, 1730, 556, 60, 220, 825, 2430, 5040, 7586, 7483, 4175, 1077, 88, 286, 1210, 4125, 10242, 19374, 25774, 21631, 10077 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts ...4...10....20.....35......56.......84......120.......165.......220........286 ...6...20....50....105.....196......336......540.......825......1210.......1716 ...9...40...125....315.....686.....1344.....2430......4125......6655......10296 ..13...76...295....889....2254.....5040....10242.....19305.....34243......57772 ..19..147...711...2567....7586....19374....44274.....92697....180829.....332761 ..28..287..1730...7483...25774....75180...193194....449295....963886....1934647 ..41..556..4175..21631...86828...289248...835812...2159025...5093737...11151140 ..60.1077.10077..62547..292621..1113348..3617703..10380183..26932543...64309245 ..88.2091.24377.181255..988303..4294574.15692003..50011289.142701909..371651553 .129.4057.58928.524877.3335451.16553380.68014233.240772037.755538278.2146210209 LINKS R. H. Hardin, Table of n, a(n) for n = 1..10011 FORMULA Empirical for column k, apparently a recurrence of order (k+1)*(k+2)/2: k=1: a(n) = a(n-1) +a(n-3) k=2: a(n) = a(n-1) +a(n-2) +2*a(n-3) -a(n-5) -a(n-6) k=3: a(n) = 2*a(n-1) +4*a(n-3) -3*a(n-4) -a(n-5) -3*a(n-6) +2*a(n-7) +a(n-9) -a(n-10) k=4: [order 15] k=5: [order 21] k=6: [order 28] k=7: [order 36] k=8: [order 45] k=9: [order 55] k=10: [order 66] k=11: [order 78] k=12: [order 91] Empirical for row n, apparently a polynomial of degree n+2: n=1: a(n) = (1/6)*n^3 + 1*n^2 + (11/6)*n + 1 n=2: a(n) = (1/12)*n^4 + (2/3)*n^3 + (23/12)*n^2 + (7/3)*n + 1 n=3: a(n) = (1/24)*n^5 + (5/12)*n^4 + (13/8)*n^3 + (37/12)*n^2 + (17/6)*n + 1 n=4: [polynomial of degree 6] n=5: [polynomial of degree 7] n=6: [polynomial of degree 8] n=7: [polynomial of degree 9] From Robert Israel, Sep 04 2019: (Start) Column k satisfies a recurrence of order (k+1)*(k+2)/2, since a(n)=e^T T^n e where T is a (k+1)*(k+2)/2 matrix and e the vector of all 1's (see proofs at A241615 and A241618). Row n is the Ehrhart polynomial of degree n+2 corresponding to the polytope {(x(1),...,x(n+2)): all x(i)>=0, x(i)+x(i+1)+x(i+2)<=1 for i=1..n}, whose vertices have all entries in {0,1}. (End) EXAMPLE Some solutions for n=5 k=4 ..1....0....2....1....0....2....0....1....0....0....0....2....1....0....1....2 ..0....0....1....3....0....0....4....2....1....0....1....1....3....0....0....1 ..0....3....0....0....0....1....0....1....3....0....0....0....0....2....1....0 ..0....0....0....1....2....0....0....0....0....0....1....0....1....1....1....2 ..2....0....3....0....0....2....0....0....0....0....2....1....0....0....0....0 ..0....1....0....1....2....1....2....0....1....0....0....1....1....0....3....1 ..0....0....0....1....0....0....2....4....2....2....0....0....2....0....0....0 MAPLE for m from 1 to 12 do   r:= [seq(seq([i, j], j=0..m-i), i=0..m)];   T[m]:= Matrix((m+1)*(m+2)/2, (m+1)*(m+2)/2, proc(i, j) if r[i][1]=r[j][2] and r[i][1]+r[i][2]+r[j][1]<=m then 1 else 0 fi end proc):   U[m, 0]:= Vector((m+1)*(m+2)/2, 1); od: R:= NULL: for i from 2 to 12 do   for j from 1 to i-1 do     U[i-j, j]:= T[i-j] . U[i-j, j-1];     R:= R, convert(U[i-j, j], `+`) od od: R; # Robert Israel, Sep 04 2019 CROSSREFS Column 1 is A000930(n+4) Row 1 is A000292(n+1) Row 2 is A002415(n+2) Row 3 is A006414 Row 4 is A114244 Sequence in context: A303052 A003564 A205016 * A129531 A298264 A014476 Adjacent sequences:  A241616 A241617 A241618 * A241620 A241621 A241622 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Apr 26 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 19 09:33 EST 2020. Contains 332041 sequences. (Running on oeis4.)