A212471 -id:A212471 - cp's OEIS frontend

A212465 Number of 0..3 arrays of length n+3 with sum no more than 6 in any length 4 subsequence (=50% duty cycle).

150, 486, 1597, 5211, 16649, 53553, 172980, 558743, 1801720, 5808944, 18737526, 60447764, 194984049, 628912080, 2028584905, 6543438398, 21106550023, 68080857417, 219600230083, 708339701336, 2284812500323, 7369860423165

Offset: 1

R. H. Hardin May 17 2012

nonn

Column 2 of A212471

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

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

Empirical: a(n) = 2*a(n-1) +3*a(n-2) +17*a(n-4) -8*a(n-5) -42*a(n-6) -8*a(n-7) -59*a(n-8) +26*a(n-9) +147*a(n-10) +33*a(n-11) +112*a(n-12) -115*a(n-13) -293*a(n-14) -5*a(n-15) -93*a(n-16) +221*a(n-17) +370*a(n-18) -65*a(n-19) +3*a(n-20) -242*a(n-21) -279*a(n-22) +78*a(n-23) +21*a(n-24) +176*a(n-25) +184*a(n-26) -33*a(n-27) -15*a(n-28) -87*a(n-29) -132*a(n-30) -7*a(n-31) +36*a(n-32) +35*a(n-33) +69*a(n-34) +5*a(n-35) -30*a(n-36) -10*a(n-37) -20*a(n-38) +10*a(n-40) +a(n-41) +2*a(n-42) -a(n-44)

A212466 Number of 0..3 arrays of length n+5 with sum no more than 9 in any length 6 subsequence (=50% duty cycle).

Original entry on oeis.org

2338, 7862, 27024, 93308, 321320, 1098260, 3708268, 12564894, 42730092, 145559900, 495992448, 1689131389, 5747566618, 19552052026, 66524165343, 226393294930, 770536024747, 2622515229619, 8925194014628, 30373724176979

Offset: 1

R. H. Hardin May 17 2012

nonn

Column 3 of A212471

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

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

A212467 Number of 0..3 arrays of length n+7 with sum no more than 12 in any length 8 subsequence (=50% duty cycle).

Original entry on oeis.org

36814, 126606, 445780, 1581686, 5622580, 19960518, 70600212, 248263590, 865983608, 3027296124, 10612842491, 37272366925, 131018316920, 460663150544, 1619367566685, 5689883208343, 19982014129382, 70158722229804

Offset: 1

R. H. Hardin May 17 2012

nonn

Column 4 of A212471

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

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

A212468 Number of 0..3 arrays of length n+9 with sum no more than 15 in any length 10 subsequence (=50% duty cycle).

Original entry on oeis.org

582440, 2034200, 7274268, 26242268, 95010466, 344305566, 1246724695, 4504766041, 16223101320, 58162431112, 207319630999, 740101423056, 2647902413670, 9488805055639, 34037887492235, 122166508976307

Offset: 1

R. H. Hardin May 17 2012

nonn

Column 5 of A212471

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

R. H. Hardin, Table of n, a(n) for n = 1..56

A212469 Number of 0..3 arrays of length n+11 with sum no more than 18 in any length 12 subsequence (=50% duty cycle).

Original entry on oeis.org

9240426, 32644314, 118029501, 430682205, 1578372444, 5795798788, 21292987433, 78186208521, 286703599009, 1049119428341, 3828209603876, 13919545400124, 50392127733527, 182633247168566, 663071942478215, 2410713609407184

Offset: 1

R. H. Hardin May 17 2012

nonn

Column 6 of A212471

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

R. H. Hardin, Table of n, a(n) for n = 1..37

A212470 Number of 0..3 arrays of length n+13 with sum no more than 21 in any length 14 subsequence (=50% duty cycle).

Original entry on oeis.org

146861788, 523487828, 1908601444, 7023308036, 25966120647, 96239314549, 357117150362, 1325550644016, 4918335298665, 18232047941771, 67489103954016, 249349516426188, 919083218908202, 3377977784235134, 12373106402582424

Offset: 1

R. H. Hardin May 17 2012

nonn

Column 7 of A212471

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

R. H. Hardin, Table of n, a(n) for n = 1..36

A212472 Number of 0..3 arrays of length 2n with sum no more than 3n in any length 2n subsequence (=50% duty cycle).

Original entry on oeis.org

10, 150, 2338, 36814, 582440, 9240426, 146861788, 2337014158, 37222215640, 593246686360, 9460081927746, 150915638082466, 2408347433725048, 38443582673708348, 613802451466325528, 9802073528030277518

Offset: 1

R. H. Hardin May 17 2012

nonn

Row 1 of A212471

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

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

A212473 Number of 0..3 arrays of length 2n+1 with sum no more than 3n in any length 2n subsequence (=50% duty cycle).

Original entry on oeis.org

30, 486, 7862, 126606, 2034200, 32644314, 523487828, 8390738062, 134446993320, 2153764911576, 34495886876214, 552428007496418, 8845775486728392, 141630619844515292, 2267494906950636872, 36300174404152871822

Offset: 1

R. H. Hardin May 17 2012

nonn

Row 2 of A212471

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

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

A212474 Number of 0..3 arrays of length 2n+2 with sum no more than 3n in any length 2n subsequence (=50% duty cycle).

Original entry on oeis.org

85, 1597, 27024, 445780, 7274268, 118029501, 1908601444, 30794657082, 496095308012, 7983014938756, 128351434757356, 2062286003105664, 33118464621596452, 531627920798750598, 8530886270887938488

Offset: 1

R. H. Hardin, May 17 2012

nonn

Row 3 of A212471.

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

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

Cf. A212471.

A212475 Number of 0..3 arrays of length 2n+3 with sum no more than 3n in any length 2n subsequence (=50% duty cycle).

Original entry on oeis.org

246, 5211, 93308, 1581686, 26242268, 430682205, 7023308036, 114062278982, 1847205725100, 29854017540652, 481755564098784, 7764949351300178, 125039067197089316, 2011992600375317822, 32354843213417739992

Offset: 1

R. H. Hardin May 17 2012

nonn

Row 4 of A212471

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

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

cp's OEIS Frontend

A212465 Number of 0..3 arrays of length n+3 with sum no more than 6 in any length 4 subsequence (=50% duty cycle).

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Formula

A212466 Number of 0..3 arrays of length n+5 with sum no more than 9 in any length 6 subsequence (=50% duty cycle).

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A212467 Number of 0..3 arrays of length n+7 with sum no more than 12 in any length 8 subsequence (=50% duty cycle).

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A212468 Number of 0..3 arrays of length n+9 with sum no more than 15 in any length 10 subsequence (=50% duty cycle).

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A212469 Number of 0..3 arrays of length n+11 with sum no more than 18 in any length 12 subsequence (=50% duty cycle).

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A212470 Number of 0..3 arrays of length n+13 with sum no more than 21 in any length 14 subsequence (=50% duty cycle).

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A212472 Number of 0..3 arrays of length 2*n with sum no more than 3*n in any length 2n subsequence (=50% duty cycle).

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A212473 Number of 0..3 arrays of length 2*n+1 with sum no more than 3*n in any length 2n subsequence (=50% duty cycle).

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A212474 Number of 0..3 arrays of length 2*n+2 with sum no more than 3*n in any length 2n subsequence (=50% duty cycle).

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Crossrefs

A212475 Number of 0..3 arrays of length 2*n+3 with sum no more than 3*n in any length 2n subsequence (=50% duty cycle).

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A212472 Number of 0..3 arrays of length 2n with sum no more than 3n in any length 2n subsequence (=50% duty cycle).

A212473 Number of 0..3 arrays of length 2n+1 with sum no more than 3n in any length 2n subsequence (=50% duty cycle).

A212474 Number of 0..3 arrays of length 2n+2 with sum no more than 3n in any length 2n subsequence (=50% duty cycle).

A212475 Number of 0..3 arrays of length 2n+3 with sum no more than 3n in any length 2n subsequence (=50% duty cycle).