A246737 -id:A246737 - cp's OEIS frontend

A246732 Number of length n+4 0..3 arrays with no pair in any consecutive five terms totalling exactly 3.

124, 260, 548, 1156, 2436, 5132, 10812, 22780, 47996, 101124, 213060, 448900, 945796, 1992716, 4198492, 8845884, 18637564, 39267844, 82734180, 174314244, 367266052, 773799948, 1630334076, 3434982396, 7237230844, 15248261636

Offset: 1

R. H. Hardin, Sep 02 2014

nonn

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

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

Column 3 of A246737.

Empirical: a(n) = 2*a(n-1) + a(n-4).

Empirical g.f.: 4*x*(31 + 3*x + 7*x^2 + 15*x^3) / (1 - 2*x - x^4). - Colin Barker, Nov 06 2018

A246733 Number of length n+4 0..4 arrays with no pair in any consecutive five terms totalling exactly 4.

Original entry on oeis.org

424, 1096, 2884, 7612, 19992, 52112, 135776, 354428, 926912, 2426008, 6344712, 16581304, 43323852, 113217276, 295956684, 773719596, 2022600900, 5286817120, 13818445276, 36118847720, 94411371892, 246786721208, 645084592792

Offset: 1

R. H. Hardin, Sep 02 2014

nonn

Column 4 of A246737

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

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

Empirical: a(n) = 2*a(n-1) +a(n-4) +24*a(n-5) +2*a(n-6) +5*a(n-7) +11*a(n-8) -8*a(n-10) -2*a(n-11) +3*a(n-12) +a(n-15) +a(n-16)

A246734 Number of length n+4 0..5 arrays with no pair in any consecutive five terms totalling exactly 5.

Original entry on oeis.org

1566, 5430, 18966, 66294, 231414, 807630, 2818830, 9838974, 34342350, 119869158, 418392870, 1460364774, 5097280614, 17791629822, 62100187038, 216755476782, 756566753022, 2640732594966, 9217254934326, 32172052811478, 112293843388758

Offset: 1

R. H. Hardin, Sep 02 2014

nonn

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

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

Column 5 of A246737.

Empirical: a(n) = 3*a(n-1) + a(n-2) + a(n-3) + 5*a(n-4) + a(n-5) - a(n-6) - a(n-7).

Empirical g.f.: 6*x*(261 + 122*x + 185*x^2 + 400*x^3 + 51*x^4 - 98*x^5 - 77*x^6) / ((1 + x)*(1 - 4*x + 3*x^2 - 4*x^3 - x^4 + x^6)). - Colin Barker, Nov 06 2018

A246735 Number of length n+4 0..6 arrays with no pair in any consecutive five terms totalling exactly 6.

Original entry on oeis.org

3876, 15960, 66378, 276762, 1152576, 4791012, 19906740, 82727094, 343911336, 1430080296, 5946396012, 24722787264, 102780120750, 427285990662, 1776417823830, 7385542897866, 30705819911322, 127659940718424

Offset: 1

R. H. Hardin, Sep 02 2014

nonn

Column 6 of A246737.

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

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

Cf. A246737.

Empirical: a(n) = 3*a(n-1) +a(n-2) +a(n-3) +5*a(n-4) +202*a(n-5) +94*a(n-6) +129*a(n-7) +278*a(n-8) +35*a(n-9) -197*a(n-10) -164*a(n-11) +272*a(n-12) +119*a(n-13) -9*a(n-14) +17*a(n-15) +158*a(n-16) +27*a(n-17) -19*a(n-18) -18*a(n-19) -a(n-20) -2*a(n-21) +2*a(n-22) +a(n-23).

A246736 Number of length n+4 0..7 arrays with no pair in any consecutive five terms totalling exactly 7.

Original entry on oeis.org

9368, 47432, 241544, 1231304, 6272072, 31944440, 162700376, 828690200, 4220813912, 21498069128, 109497066248, 557706305672, 2840590647176, 14468108341688, 73691067738968, 375334033262552, 1911705731599640

Offset: 1

R. H. Hardin, Sep 02 2014

nonn

Column 7 of A246737

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

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

Empirical: a(n) = 4*a(n-1) +4*a(n-2) +4*a(n-3) +18*a(n-4) +12*a(n-5) -4*a(n-7) -a(n-8)

A246738 Number of length 1+4 0..n arrays with no pair in any consecutive five terms totalling exactly n.

Original entry on oeis.org

2, 12, 124, 424, 1566, 3876, 9368, 18768, 36250, 63100, 106452, 168312, 259574, 383124, 554416, 777376, 1072818, 1445868, 1923500, 2512200, 3245902, 4132612, 5214024, 6499824, 8040266, 9846876, 11979268, 14450968, 17331750, 20637300

Offset: 1

R. H. Hardin, Sep 02 2014

nonn

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

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

Row 1 of A246737.

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 06 2018: (Start)
G.f.: 2*x*(1 + 3*x + 44*x^2 + 34*x^3 + 189*x^4 + 43*x^5 + 166*x^6) / ((1 - x)^6*(1 + x)^3).
a(n) = 10*n - 20*n^2 + 15*n^3 - 5*n^4 + n^5 for n even.
a(n) = 16 - 15*n - 10*n^2 + 15*n^3 - 5*n^4 + n^5 for n odd.
(End)

A246739 Number of length 2+4 0..n arrays with no pair in any consecutive five terms totalling exactly n.

Original entry on oeis.org

2, 16, 260, 1096, 5430, 15960, 47432, 109552, 246890, 483520, 920652, 1606776, 2735390, 4392136, 6907280, 10419040, 15447762, 22202352, 31455380, 43507240, 59453702, 79710136, 105775320, 138205776, 178991930, 228860320, 290390492

Offset: 1

R. H. Hardin, Sep 02 2014

nonn

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

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

Row 2 of A246737.

Empirical: a(n) = 3*a(n-1) + a(n-2) - 11*a(n-3) + 6*a(n-4) + 14*a(n-5) - 14*a(n-6) - 6*a(n-7) + 11*a(n-8) - a(n-9) - 3*a(n-10) + a(n-11).
Conjectures from Colin Barker, Nov 06 2018: (Start)
G.f.: 2*x*(1 + 5*x + 105*x^2 + 161*x^3 + 1023*x^4 + 655*x^5 + 2211*x^6 + 523*x^7 + 1076*x^8) / ((1 - x)^7*(1 + x)^4).
a(n) = -58*n + 111*n^2 - 87*n^3 + 36*n^4 - 8*n^5 + n^6 for n even.
a(n) = -70 + 80*n + 34*n^2 - 71*n^3 + 36*n^4 - 8*n^5 + n^6 for n odd.
(End)

A246740 Number of length 3+4 0..n arrays with no pair in any consecutive five terms totalling exactly n.

Original entry on oeis.org

2, 22, 548, 2884, 18966, 66378, 241544, 643048, 1687850, 3716830, 7980972, 15368172, 28868798, 50412754, 86141456, 139758928, 222590034, 341128998, 514651700, 753789460, 1089386342, 1537935322, 2146429848, 2939373624

Offset: 1

R. H. Hardin, Sep 02 2014

nonn

Row 3 of A246737

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

R. H. Hardin, Table of n, a(n) for n = 1..71

Empirical: a(n) = 3*a(n-1) +2*a(n-2) -14*a(n-3) +5*a(n-4) +25*a(n-5) -20*a(n-6) -20*a(n-7) +25*a(n-8) +5*a(n-9) -14*a(n-10) +2*a(n-11) +3*a(n-12) -a(n-13)

A246741 Number of length 4+4 0..n arrays with no pair in any consecutive five terms totalling exactly n.

Original entry on oeis.org

2, 30, 1156, 7612, 66294, 276762, 1231304, 3780600, 11549290, 28599190, 69230412, 147079860, 304811486, 578865042, 1074611344, 1875204592, 3208049874, 5242291470, 8421730580, 13061681580, 19963508422, 29676180490, 43560086616

Offset: 1

R. H. Hardin, Sep 02 2014

nonn

Row 4 of A246737

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

R. H. Hardin, Table of n, a(n) for n = 1..69

Empirical: a(n) = 3*a(n-1) +3*a(n-2) -17*a(n-3) +3*a(n-4) +39*a(n-5) -25*a(n-6) -45*a(n-7) +45*a(n-8) +25*a(n-9) -39*a(n-10) -3*a(n-11) +17*a(n-12) -3*a(n-13) -3*a(n-14) +a(n-15)

A246742 Number of length 5+4 0..n arrays with no pair in any consecutive five terms totalling exactly n.

Original entry on oeis.org

2, 40, 2436, 19992, 231414, 1152576, 6272072, 22219408, 79002090, 220032120, 600454092, 1407554280, 3218159966, 6646694992, 13405336464, 25160170656, 46234874322, 80560371528, 137811490580, 226332464440, 365838595782

Offset: 1

R. H. Hardin, Sep 02 2014

nonn

Row 5 of A246737

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

R. H. Hardin, Table of n, a(n) for n = 1..66

Empirical: a(n) = 3*a(n-1) +4*a(n-2) -20*a(n-3) +56*a(n-5) -28*a(n-6) -84*a(n-7) +70*a(n-8) +70*a(n-9) -84*a(n-10) -28*a(n-11) +56*a(n-12) -20*a(n-14) +4*a(n-15) +3*a(n-16) -a(n-17)

cp's OEIS Frontend

A246732 Number of length n+4 0..3 arrays with no pair in any consecutive five terms totalling exactly 3.

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A246733 Number of length n+4 0..4 arrays with no pair in any consecutive five terms totalling exactly 4.

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A246734 Number of length n+4 0..5 arrays with no pair in any consecutive five terms totalling exactly 5.

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A246735 Number of length n+4 0..6 arrays with no pair in any consecutive five terms totalling exactly 6.

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A246736 Number of length n+4 0..7 arrays with no pair in any consecutive five terms totalling exactly 7.

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A246738 Number of length 1+4 0..n arrays with no pair in any consecutive five terms totalling exactly n.

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A246739 Number of length 2+4 0..n arrays with no pair in any consecutive five terms totalling exactly n.

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A246740 Number of length 3+4 0..n arrays with no pair in any consecutive five terms totalling exactly n.

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A246741 Number of length 4+4 0..n arrays with no pair in any consecutive five terms totalling exactly n.

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A246742 Number of length 5+4 0..n arrays with no pair in any consecutive five terms totalling exactly n.

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