cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A225349 Number of 9Xn -1,1 arrays such that the sum over i=1..9,j=1..n of i*x(i,j) is zero, the sum of x(i,j) is zero, and rows are nondecreasing (number of ways to distribute n-across galley oarsmen left-right at 9 fore-aft positions so that there are no turning moments on the ship).

Original entry on oeis.org

0, 181, 0, 6095, 0, 63121, 0, 364051, 0, 1478059, 0, 4749875, 0, 12917383, 0, 30996867, 0, 67483509, 0, 135917019, 0, 256859575, 0, 460336079, 0, 788783775, 0, 1300561813, 0, 2074066679, 0, 3212505371, 0, 4849371247, 0, 7154674999, 0, 10341975199, 0
Offset: 1

Views

Author

R. H. Hardin May 05 2013

Keywords

Comments

Row 9 of A225345

Examples

			Some solutions for n=4
.-1.-1..1..1...-1.-1..1..1...-1.-1.-1..1...-1.-1..1..1...-1.-1..1..1
.-1.-1.-1.-1...-1.-1.-1.-1....1..1..1..1...-1.-1..1..1...-1.-1.-1..1
.-1.-1..1..1....1..1..1..1...-1.-1..1..1...-1..1..1..1....1..1..1..1
..1..1..1..1...-1.-1..1..1...-1.-1..1..1...-1.-1.-1.-1...-1..1..1..1
.-1.-1..1..1....1..1..1..1...-1.-1..1..1....1..1..1..1...-1.-1.-1.-1
.-1..1..1..1...-1.-1.-1.-1...-1.-1.-1..1...-1.-1..1..1...-1.-1..1..1
.-1..1..1..1...-1.-1.-1..1...-1.-1.-1..1...-1.-1.-1.-1...-1.-1.-1.-1
.-1.-1.-1..1....1..1..1..1...-1.-1.-1..1...-1.-1..1..1....1..1..1..1
.-1.-1.-1..1...-1.-1.-1..1....1..1..1..1...-1..1..1..1...-1.-1..1..1
		

Formula

Empirical: a(n) = 2*a(n-2) -a(n-6) -a(n-10) +a(n-12) -a(n-14) +a(n-18) +a(n-20) +a(n-24) -2*a(n-26) -2*a(n-32) +a(n-34) +a(n-38) +a(n-40) -a(n-44) +a(n-46) -a(n-48) -a(n-52) +2*a(n-56) -a(n-58)

A225350 Number of 10Xn -1,1 arrays such that the sum over i=1..10,j=1..n of i*x(i,j) is zero, the sum of x(i,j) is zero, and rows are nondecreasing (number of ways to distribute n-across galley oarsmen left-right at 10 fore-aft positions so that there are no turning moments on the ship).

Original entry on oeis.org

0, 443, 0, 24893, 0, 360909, 0, 2676331, 0, 13280209, 0, 50435657, 0, 158259755, 0, 430394067, 0, 1047240813, 0, 2331232209, 0, 4825180007, 0, 9399464741, 0, 17394354077, 0, 30804515135, 0, 52513235123, 0, 86584738985, 0, 138623327831, 0
Offset: 1

Views

Author

R. H. Hardin May 05 2013

Keywords

Comments

Row 10 of A225345

Examples

			Some solutions for n=4
..1..1..1..1...-1.-1.-1.-1...-1.-1.-1..1...-1.-1.-1..1...-1.-1.-1.-1
.-1.-1.-1.-1....1..1..1..1...-1..1..1..1...-1..1..1..1...-1..1..1..1
.-1.-1.-1..1...-1.-1.-1.-1...-1..1..1..1...-1.-1.-1..1...-1.-1..1..1
.-1..1..1..1....1..1..1..1...-1.-1.-1..1...-1.-1..1..1....1..1..1..1
..1..1..1..1....1..1..1..1...-1.-1..1..1...-1..1..1..1...-1..1..1..1
.-1.-1.-1.-1...-1..1..1..1...-1.-1..1..1...-1..1..1..1...-1.-1.-1.-1
.-1.-1.-1..1...-1.-1.-1.-1...-1..1..1..1...-1..1..1..1...-1.-1.-1..1
.-1.-1.-1..1...-1.-1.-1..1...-1.-1.-1..1...-1.-1.-1..1....1..1..1..1
..1..1..1..1...-1.-1.-1.-1...-1.-1.-1..1...-1.-1.-1.-1...-1.-1..1..1
.-1.-1..1..1....1..1..1..1...-1..1..1..1...-1..1..1..1...-1.-1.-1..1
		

Formula

Empirical: a(n) = a(n-2) +a(n-4) -a(n-10) -a(n-14) -a(n-20) +2*a(n-24) +a(n-26) +a(n-28) +a(n-30) -a(n-34) -a(n-36) -a(n-38) -2*a(n-40) -a(n-42) -a(n-44) +a(n-46) +a(n-48) +2*a(n-50) +a(n-52) +a(n-54) +a(n-56) -a(n-60) -a(n-62) -a(n-64) -2*a(n-66) +a(n-70) +a(n-76) +a(n-80) -a(n-86) -a(n-88) +a(n-90)

A225351 Number of 11Xn -1,1 arrays such that the sum over i=1..11,j=1..n of i*x(i,j) is zero, the sum of x(i,j) is zero, and rows are nondecreasing (number of ways to distribute n-across galley oarsmen left-right at 11 fore-aft positions so that there are no turning moments on the ship).

Original entry on oeis.org

0, 1113, 0, 103583, 0, 2102597, 0, 20044255, 0, 121558241, 0, 545572495, 0, 1975264495, 0, 6087969941, 0, 16555930825, 0, 40733826807, 0, 92339940289, 0, 195519292147, 0, 390766431925, 0, 743286869427, 0, 1354483437063, 0
Offset: 1

Views

Author

R. H. Hardin May 05 2013

Keywords

Comments

Row 11 of A225345

Examples

			Some solutions for n=4
.-1.-1.-1..1....1..1..1..1...-1.-1.-1..1....1..1..1..1...-1..1..1..1
.-1.-1..1..1...-1.-1.-1..1...-1.-1..1..1...-1.-1.-1..1...-1.-1.-1.-1
..1..1..1..1...-1.-1.-1..1...-1.-1..1..1...-1.-1..1..1...-1..1..1..1
.-1.-1..1..1...-1..1..1..1...-1..1..1..1...-1.-1.-1..1...-1.-1..1..1
.-1.-1.-1.-1...-1.-1..1..1...-1.-1..1..1...-1.-1..1..1...-1.-1.-1..1
..1..1..1..1...-1.-1.-1..1...-1.-1..1..1...-1.-1..1..1...-1..1..1..1
.-1.-1..1..1...-1.-1..1..1...-1..1..1..1...-1.-1.-1.-1...-1..1..1..1
.-1.-1..1..1...-1.-1.-1.-1...-1.-1.-1..1...-1.-1..1..1...-1.-1.-1..1
.-1.-1.-1..1...-1.-1..1..1...-1..1..1..1....1..1..1..1...-1..1..1..1
.-1.-1.-1.-1...-1..1..1..1...-1.-1..1..1...-1.-1..1..1...-1.-1.-1.-1
..1..1..1..1...-1..1..1..1...-1.-1.-1..1...-1.-1..1..1...-1..1..1..1
		

Formula

Empirical: a(n) = 2*a(n-4) +a(n-6) -a(n-12) -3*a(n-14) -2*a(n-16) +3*a(n-24) +4*a(n-26) +2*a(n-28) +3*a(n-30) +2*a(n-32) -3*a(n-34) -5*a(n-36) -4*a(n-38) -5*a(n-40) -4*a(n-42) -a(n-44) +2*a(n-46) +4*a(n-48) +6*a(n-50) +6*a(n-52) +4*a(n-54) +2*a(n-56) -a(n-58) -4*a(n-60) -5*a(n-62) -4*a(n-64) -5*a(n-66) -3*a(n-68) +2*a(n-70) +3*a(n-72) +2*a(n-74) +4*a(n-76) +3*a(n-78) -2*a(n-86) -3*a(n-88) -a(n-90) +a(n-96) +2*a(n-98) -a(n-102)

A225352 Number of 12Xn -1,1 arrays such that the sum over i=1..12,j=1..n of i*x(i,j) is zero, the sum of x(i,j) is zero, and rows are nondecreasing (number of ways to distribute n-across galley oarsmen left-right at 12 fore-aft positions so that there are no turning moments on the ship).

Original entry on oeis.org

58, 2837, 47990, 437763, 2680534, 12439855, 47084448, 152452967, 436320984, 1129965973, 2694285574, 5993361143, 12566218452, 25037146431, 47716202440, 87454967053, 154837885246, 265807450011, 443841357932, 722822838305
Offset: 1

Views

Author

R. H. Hardin May 05 2013

Keywords

Comments

Row 12 of A225345

Examples

			Some solutions for n=4
.-1.-1.-1..1...-1.-1.-1.-1...-1.-1.-1..1...-1.-1.-1.-1...-1.-1.-1..1
.-1.-1.-1..1...-1.-1.-1..1...-1.-1.-1..1...-1..1..1..1...-1.-1.-1.-1
.-1.-1..1..1...-1..1..1..1....1..1..1..1...-1.-1..1..1...-1..1..1..1
.-1..1..1..1....1..1..1..1...-1..1..1..1....1..1..1..1...-1..1..1..1
..1..1..1..1...-1.-1..1..1...-1..1..1..1...-1.-1.-1..1...-1.-1..1..1
.-1..1..1..1....1..1..1..1...-1.-1.-1..1...-1.-1..1..1...-1.-1.-1..1
.-1.-1..1..1...-1.-1.-1.-1...-1.-1.-1.-1...-1.-1..1..1....1..1..1..1
.-1.-1.-1..1....1..1..1..1...-1.-1..1..1....1..1..1..1...-1..1..1..1
.-1.-1.-1.-1...-1.-1.-1..1....1..1..1..1...-1.-1.-1.-1....1..1..1..1
..1..1..1..1...-1..1..1..1...-1.-1.-1.-1...-1..1..1..1...-1..1..1..1
.-1.-1.-1..1...-1.-1.-1.-1....1..1..1..1...-1.-1.-1..1...-1.-1.-1.-1
.-1.-1..1..1...-1.-1..1..1...-1.-1.-1..1...-1.-1..1..1...-1.-1.-1.-1
		

Formula

Empirical: a(n) = a(n-1) +a(n-2) -a(n-5) -a(n-7) +a(n-14) +2*a(n-15) +a(n-16) -a(n-19) -a(n-20) -a(n-21) -2*a(n-22) -a(n-23) -a(n-24) -a(n-26) +2*a(n-27) +2*a(n-28) +2*a(n-29) +2*a(n-30) +a(n-31) +a(n-32) -a(n-34) -a(n-35) -2*a(n-36) -2*a(n-37) -2*a(n-38) -2*a(n-39) +a(n-40) +a(n-42) +a(n-43) +2*a(n-44) +a(n-45) +a(n-46) +a(n-47) -a(n-50) -2*a(n-51) -a(n-52) +a(n-59) +a(n-61) -a(n-64) -a(n-65) +a(n-66)
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