A200330 Number of 0..n arrays x(0..6) of 7 elements with zero 3rd differences.
2, 3, 4, 5, 6, 13, 20, 27, 36, 49, 62, 81, 100, 119, 146, 177, 208, 247, 286, 329, 380, 435, 490, 555, 624, 697, 780, 867, 954, 1059, 1164, 1273, 1394, 1519, 1648, 1797, 1946, 2099, 2264, 2441, 2618, 2817, 3016, 3219, 3444, 3677, 3910, 4165, 4420, 4687, 4974
Offset: 1
Keywords
Examples
All solutions for n=6 ..6....4....0....6....1....3....3....5....0....2....6....0....3 ..6....4....0....3....1....5....3....5....3....2....5....1....1 ..6....4....0....1....1....6....3....5....5....2....4....2....0 ..6....4....0....0....1....6....3....5....6....2....3....3....0 ..6....4....0....0....1....5....3....5....6....2....2....4....1 ..6....4....0....1....1....3....3....5....5....2....1....5....3 ..6....4....0....3....1....0....3....5....3....2....0....6....6
Links
- R. H. Hardin, Table of n, a(n) for n = 1..200
Formula
Empirical: a(n) = a(n-1) -a(n-3) +a(n-4) +a(n-9) -a(n-11) +a(n-12) -a(n-14) +a(n-15) -a(n-16) +a(n-18) -2*a(n-19) +a(n-20) -a(n-22) +a(n-23) -a(n-24) +a(n-26) -a(n-27) +a(n-29) +a(n-34) -a(n-35) +a(n-37) -a(n-38).
Empirical: G.f.: -x*(-2 -x -x^2 -35*x^20 -27*x^21 -29*x^22 -24*x^23 -18*x^24 -19*x^25 -2*x^30- 2*x^31 -2*x^32 -2*x^33 -x^35 -x^36 +x^37 -14*x^26 -8*x^27 -9*x^28 -8*x^29 -3*x^3 -2*x^4 -8*x^5 -8*x^6 -8*x^7 -16*x^8 -18*x^9 -17*x^10 -26*x^11 -28*x^12 -27*x^13 -36*x^14 -32*x^15 -33*x^16 -41*x^17 -31*x^18 -34*x^19) / ( (x^2-x+1) *(x^4-x^3+x^2-x+1) *(x^6+x^3+1) *(x^8-x^7+x^5-x^4+x^3-x+1)* (1+x)^2 *(1+x+x^2)^2 *(x^4+x^3+x^2+x+1)^2 *(x-1)^4 ). - R. J. Mathar, Mar 07 2015
Comments