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

1,1

Comments

Row 4 of A200329

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

Example

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

Crossrefs

Sequence in context: A255261 A181303 A276529 * A121433 A317778 A259541

Adjacent sequences: A200327 A200328 A200329 * A200331 A200332 A200333

Keyword

nonn

Author

R. H. Hardin Nov 16 2011

Status

approved