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.

Showing 1-10 of 13 results. Next

A250777 Number of (n+1) X (2+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

21, 46, 96, 196, 396, 796, 1596, 3196, 6396, 12796, 25596, 51196, 102396, 204796, 409596, 819196, 1638396, 3276796, 6553596, 13107196, 26214396, 52428796, 104857596, 209715196, 419430396, 838860796, 1677721596, 3355443196
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 2 of A250783.

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2); a(n) = 25*2^(n-1) - 4.
Empirical g.f.: x*(21 - 17*x) / ((1 - x)*(1 - 2*x)). - Colin Barker, Nov 19 2018

A250778 Number of (n+1) X (3+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

46, 106, 230, 482, 990, 2010, 4054, 8146, 16334, 32714, 65478, 131010, 262078, 524218, 1048502, 2097074, 4194222, 8388522, 16777126, 33554338, 67108766, 134217626, 268435350, 536870802, 1073741710, 2147483530, 4294967174
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 3 of A250783.

Formula

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).
Conjectures from Colin Barker, Nov 19 2018: (Start)
G.f.: 2*x*(23 - 39*x + 18*x^2) / ((1 - x)^2*(1 - 2*x)).
a(n) = 2^(5+n) - 4*n - 14.
(End)

A250779 Number of (n+1) X (4+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

99, 238, 534, 1152, 2426, 5028, 10306, 20960, 42394, 85420, 171666, 344392, 690122, 1381908, 2765858, 5534192, 11071354, 22146236, 44296626, 88598104, 177201834, 354410148, 708827714, 1417663872, 2835337306, 5670685388, 11341382866
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 4 of A250783.

Formula

Empirical: a(n) = 6*a(n-1) - 14*a(n-2) + 16*a(n-3) - 9*a(n-4) + 2*a(n-5).
Conjectures from Colin Barker, Nov 19 2018: (Start)
G.f.: x*(99 - 356*x + 492*x^2 - 304*x^3 + 73*x^4) / ((1 - x)^4*(1 - 2*x)).
a(n) = (-288 + 507*2^n - 116*n - 12*n^2 - 4*n^3) / 6.
(End)

A250780 Number of (n+1) X (5+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

209, 518, 1194, 2640, 5688, 12036, 25126, 51904, 106344, 216500, 438614, 885336, 1782168, 3580356, 7182678, 14395024, 28829560, 57711060, 115489574, 231065768, 462241608, 924621732, 1849416198, 3699045984, 7398353992, 14797027060
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 5 of A250783.

Formula

Empirical: a(n) = 8*a(n-1) - 27*a(n-2) + 50*a(n-3) - 55*a(n-4) + 36*a(n-5) - 13*a(n-6) + 2*a(n-7).
Conjectures from Colin Barker, Nov 19 2018: (Start)
G.f.: x*(209 - 1154*x + 2693*x^2 - 3376*x^3 + 2401*x^4 - 922*x^5 + 153*x^6) / ((1 - x)^6*(1 - 2*x)).
a(n) = (9/2)*(49*2^n-32) - (374*n)/5 - 9*n^2 - (25*n^3)/6 - n^5/30.
(End)

A250781 Number of (n+1) X (6+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

436, 1106, 2604, 5882, 12950, 27986, 59590, 125334, 260916, 538538, 1103752, 2249266, 4562698, 9222258, 18588322, 37386830, 75076376, 150582730, 301768276, 604371338, 1209885342, 2421317714, 4844708318, 9692167046, 19387949788
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 6 of A250783.

Formula

Empirical: a(n) = 10*a(n-1) - 44*a(n-2) + 112*a(n-3) - 182*a(n-4) + 196*a(n-5) - 140*a(n-6) + 64*a(n-7) - 17*a(n-8) + 2*a(n-9).
Conjectures from Colin Barker, Nov 19 2018: (Start)
G.f.: 2*x*(218 - 1627*x + 5364*x^2 - 10163*x^3 + 12093*x^4 - 9259*x^5 + 4469*x^6 - 1253*x^7 + 160*x^8) / ((1 - x)^8*(1 - 2*x)).
a(n) = (2520*(289*2^n-209) - 314796*n - 41972*n^2 - 23779*n^3 + 385*n^4 - 364*n^5 + 7*n^6 - n^7) / 1260.
(End)

A250782 Number of (n+1) X (7+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

901, 2326, 5568, 12796, 28692, 63184, 137082, 293588, 621664, 1303276, 2708612, 5587548, 11454008, 23356632, 47422730, 95949660, 193592124, 389742628, 783299900, 1572215204, 3152596828, 6316933760, 12650561098, 25324612868
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 7 of A250783.

Formula

Empirical: a(n) = 12*a(n-1) - 65*a(n-2) + 210*a(n-3) - 450*a(n-4) + 672*a(n-5) - 714*a(n-6) + 540*a(n-7) - 285*a(n-8) + 100*a(n-9) - 21*a(n-10) + 2*a(n-11).
Conjectures from Colin Barker, Nov 19 2018: (Start)
G.f.: x*(901 - 8486*x + 36221*x^2 - 92040*x^3 + 154050*x^4 - 177432*x^5 + 142536*x^6 - 79028*x^7 + 29083*x^8 - 6482*x^9 + 681*x^10) / ((1 - x)^10*(1 - 2*x)).
a(n) = (45360*(3025*2^n-2344) - 70509024*n - 9423432*n^2 - 6541100*n^3 + 254142*n^4 - 151725*n^5 + 6552*n^6 - 870*n^7 + 18*n^8 - n^9) / 90720.
(End)

A250784 Number of (2+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

18, 46, 106, 238, 518, 1106, 2326, 4838, 9978, 20446, 41686, 84658, 171398, 346166, 697786, 1404398, 2823078, 5669266, 11375926, 22812358, 45722618, 91603646, 183463606, 367341938, 735354918, 1471795606, 2945348026, 5893538638
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 2 of A250783.

Formula

Empirical: a(n) = 4*a(n-1) - 4*a(n-2) - a(n-3) + 2*a(n-4).
Conjectures from Colin Barker, Nov 19 2018: (Start)
G.f.: 2*x*(9 - 13*x - 3*x^2 + 8*x^3) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)).
a(n) = 2^(1-n) * (2^n*(1+11*2^n) + 2*(1-sqrt(5))^n*(-2+sqrt(5)) - 2*(1+sqrt(5))^n*(2+sqrt(5))).
(End)

A250785 Number of (3+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

36, 96, 230, 534, 1194, 2604, 5568, 11732, 24442, 50482, 103566, 211360, 429580, 870280, 1758574, 3546318, 7139858, 14356148, 28835992, 57872156, 116068226, 232660586, 466169270, 933710824, 1869642084, 3742876944, 7491567158
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 3 of A250783.

Formula

Empirical: a(n) = 5*a(n-1) - 8*a(n-2) + 3*a(n-3) + 3*a(n-4) - 2*a(n-5).
Empirical g.f.: 2*x*(18 - 42*x + 19*x^2 + 22*x^3 - 16*x^4) / ((1 - x)^2*(1 - 2*x)*(1 - x - x^2)). - Colin Barker, Nov 19 2018

A250786 Number of (4+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

72, 196, 482, 1152, 2640, 5882, 12796, 27344, 57610, 120060, 248072, 509158, 1039532, 2113580, 4283210, 8657344, 17462056, 35162842, 70712260, 142050352, 285113682, 571866796, 1146386672, 2297066582, 4601080260, 9213401692
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 4 of A250783.

Formula

Empirical: a(n) = 5*a(n-1) - 7*a(n-2) - 2*a(n-3) + 11*a(n-4) - 5*a(n-5) - 3*a(n-6) + 2*a(n-7).
Empirical g.f.: 2*x*(36 - 82*x + 3*x^2 + 129*x^3 - 73*x^4 - 43*x^5 + 32*x^6) / ((1 - x)^3*(1 + x)*(1 - 2*x)*(1 - x - x^2)). - Colin Barker, Nov 20 2018

A250787 Number of (5+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

144, 396, 990, 2426, 5688, 12950, 28692, 62274, 132890, 279864, 583196, 1205236, 2474328, 5053216, 10277030, 20831790, 42114880, 84962234, 171112172, 344149014, 691415474, 1387878796, 2783929300, 5581085336, 11183577088, 22401796180
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 5 of A250783.

Formula

Empirical: a(n) = 6*a(n-1) - 12*a(n-2) + 5*a(n-3) + 13*a(n-4) - 16*a(n-5) + 2*a(n-6) + 5*a(n-7) - 2*a(n-8).
Empirical g.f.: 2*x*(72 - 234*x + 171*x^2 + 259*x^3 - 420*x^4 + 70*x^5 + 148*x^6 - 64*x^7) / ((1 - x)^4*(1 + x)*(1 - 2*x)*(1 - x - x^2)). - Colin Barker, Nov 20 2018
Showing 1-10 of 13 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.