A245869 -id:A245869 - cp's OEIS frontend

A245875 Number of length 6+2 0..n arrays with some pair in every consecutive three terms totalling exactly n.

68, 1281, 4624, 13961, 30900, 63241, 113024, 193137, 305860, 470321, 688848, 987961, 1369844, 1869561, 2488960, 3272801, 4222404, 5393377, 6786320, 8468841, 10440628, 12782441, 15492864, 18666961, 22302020, 26508561, 31282384, 36750617

Offset: 1

R. H. Hardin, Aug 04 2014

nonn

			Some solutions for n=8:
..2....4....4....0....0....4....3....3....1....0....1....2....0....3....0....3
..6....4....1....8....8....4....6....6....7....8....8....2....7....7....8....7
..2....4....7....0....7....7....2....5....1....1....0....6....1....1....8....1
..2....8....4....6....1....1....3....3....4....7....2....2....3....1....0....0
..6....0....4....2....6....7....5....8....4....6....6....3....5....7....6....8
..5....3....4....6....2....1....5....0....5....1....3....5....3....3....2....8
..2....5....7....3....1....3....3....8....4....7....5....5....5....5....5....0
..6....4....1....2....6....5....4....0....3....4....7....3....3....5....3....5

R. H. Hardin, Table of n, a(n) for n = 1..210

Row 6 of A245869.

Empirical: a(n) = 3*a(n-1) - 8*a(n-3) + 6*a(n-4) + 6*a(n-5) - 8*a(n-6) + 3*a(n-8) - a(n-9).
Conjectures from Colin Barker, Nov 04 2018: (Start)
G.f.: x*(68 + 1077*x + 781*x^2 + 633*x^3 - 1143*x^4 - 561*x^5 + 103*x^6 + 3*x^7 - x^8) / ((1 - x)^6*(1 + x)^3).
a(n) = 1 + 22*n + 31*n^2 + 77*n^3 + 29*n^4 + n^5 for n even.
a(n) = -5 - 44*n + 10*n^2 + 77*n^3 + 29*n^4 + n^5 for n odd.
(End)

A245876 Number of length 7+2 0..n arrays with some pair in every consecutive three terms totalling exactly n.

Original entry on oeis.org

110, 2967, 12100, 40901, 97602, 214315, 404264, 727017, 1200310, 1920671, 2909100, 4309357, 6143690, 8614131, 11741392, 15797585, 20798334, 27098407, 34704020, 44065941, 55175890, 68594747, 84293880, 102959161, 124534982, 149847855

Offset: 1

R. H. Hardin, Aug 04 2014

nonn

			Some solutions for n=5:
..2....4....0....4....0....0....2....3....4....2....3....3....4....1....1....5
..2....1....5....3....2....3....4....0....1....0....3....5....3....3....0....0
..3....2....1....2....3....2....1....5....5....5....2....0....2....2....4....5
..2....3....4....3....0....5....3....0....0....3....3....1....5....5....5....2
..3....3....1....2....5....3....4....0....4....2....0....4....3....3....0....3
..3....2....2....4....3....2....1....5....1....0....5....2....2....2....5....5
..2....2....3....1....2....2....4....3....4....3....2....1....2....3....4....2
..3....3....2....0....1....3....2....2....2....2....0....3....3....2....1....0
..1....2....4....4....3....2....1....0....3....4....3....2....5....4....5....5

R. H. Hardin, Table of n, a(n) for n = 1..210

Row 7 of A245869.

Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 8*a(n-3) - 2*a(n-4) + 12*a(n-5) - 2*a(n-6) - 8*a(n-7) + 3*a(n-8) + 2*a(n-9) - a(n-10).
Conjectures from Colin Barker, Nov 05 2018: (Start)
G.f.: x*(110 + 2747*x + 5836*x^2 + 8680*x^3 + 3456*x^4 - 2178*x^5 - 1148*x^6 - 224*x^7 + 2*x^8 - x^9) / ((1 - x)^6*(1 + x)^4).
a(n) = 1 + 37*n + 43*n^2 + 126*n^3 + 89*n^4 + 9*n^5 for n even.
a(n) = 7 - 76*n - 41*n^2 + 122*n^3 + 89*n^4 + 9*n^5 for n odd.
(End)

cp's OEIS Frontend

A245875 Number of length 6+2 0..n arrays with some pair in every consecutive three terms totalling exactly n.

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