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 12 results. Next

A297757 Number of nX3 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2, 3 or 4 neighboring 1s.

Original entry on oeis.org

1, 12, 52, 186, 1045, 5685, 28565, 148681, 783104, 4082179, 21289432, 111293510, 581390557, 3036127779, 15859365566, 82842802213, 432710054944, 2260195540670, 11805906967573, 61666590418664, 322107101630217, 1682485627292574
Offset: 1

Views

Author

R. H. Hardin, Jan 05 2018

Keywords

Comments

Column 3 of A297762.

Examples

			Some solutions for n=7
..1..1..0. .0..1..1. .0..1..1. .1..1..0. .0..1..0. .0..1..1. .1..1..1
..1..1..1. .1..1..0. .1..1..0. .1..1..0. .1..1..1. .0..1..1. .0..1..0
..0..1..0. .1..1..0. .0..1..1. .0..1..1. .0..1..0. .0..1..1. .0..1..0
..0..0..0. .0..1..0. .0..1..1. .0..0..0. .1..1..1. .0..0..0. .1..0..1
..0..1..0. .1..1..0. .0..1..0. .0..1..0. .0..1..0. .0..1..0. .1..1..0
..1..1..1. .1..1..1. .0..1..1. .1..1..1. .1..1..1. .1..1..1. .0..1..1
..0..1..0. .0..0..0. .1..1..1. .0..0..0. .1..1..1. .1..1..0. .1..1..0
		

Crossrefs

Cf. A297762.

Formula

Empirical: a(n) = 3*a(n-1) +2*a(n-2) +52*a(n-3) +2*a(n-4) +27*a(n-5) -378*a(n-6) -365*a(n-7) -173*a(n-8) +386*a(n-9) +1006*a(n-10) +488*a(n-11) +468*a(n-12) +328*a(n-13) -120*a(n-14) -80*a(n-15)

A297758 Number of nX4 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2, 3 or 4 neighboring 1s.

Original entry on oeis.org

1, 31, 206, 1181, 10639, 90727, 720785, 5909241, 48847911, 400405024, 3283795151, 26976077016, 221488948284, 1818161928153, 14927447103567, 122557391321622, 1006185363901356, 8260764995494461, 67821099419523837, 556811248211302092
Offset: 1

Views

Author

R. H. Hardin, Jan 05 2018

Keywords

Comments

Column 4 of A297762.

Examples

			Some solutions for n=6
..1..1..1..0. .0..0..1..1. .0..0..0..0. .0..1..1..0. .0..0..1..0
..1..1..1..1. .0..1..1..1. .0..1..1..1. .0..1..1..0. .0..1..1..1
..0..1..0..0. .0..0..1..0. .0..0..1..0. .0..1..1..0. .0..0..1..1
..0..1..1..1. .0..1..1..1. .0..0..1..1. .0..1..1..0. .0..1..1..0
..0..1..1..0. .0..1..0..1. .0..1..1..1. .0..1..1..0. .0..1..1..0
..0..1..1..0. .0..0..1..0. .0..0..0..0. .1..1..0..0. .1..1..1..1
		

Crossrefs

Cf. A297762.

Formula

Empirical: a(n) = 5*a(n-1) +12*a(n-2) +129*a(n-3) +20*a(n-4) -547*a(n-5) -2737*a(n-6) -3239*a(n-7) +4035*a(n-8) +19926*a(n-9) +29650*a(n-10) +11984*a(n-11) -27223*a(n-12) -50924*a(n-13) -45534*a(n-14) -21444*a(n-15) +9879*a(n-16) +39144*a(n-17) +44228*a(n-18) +22820*a(n-19) -5575*a(n-20) -15128*a(n-21) -9730*a(n-22) -6130*a(n-23) -3709*a(n-24) +1233*a(n-25) +3495*a(n-26) +1422*a(n-27) -274*a(n-28) -130*a(n-29) +110*a(n-30) +7*a(n-31) -35*a(n-32) -10*a(n-33)

A297759 Number of nX5 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2, 3 or 4 neighboring 1s.

Original entry on oeis.org

1, 78, 734, 7081, 109228, 1456855, 18733087, 251641086, 3354939709, 44459037210, 591410913625, 7865974374583, 104544861995486, 1389898494780143, 18479036986992209, 245664832111845278, 3265995303275846454
Offset: 1

Views

Author

R. H. Hardin, Jan 05 2018

Keywords

Comments

Column 5 of A297762.

Examples

			Some solutions for n=5
..1..1..1..1..0. .1..1..0..0..0. .0..0..1..1..1. .0..0..1..0..0
..1..1..0..0..1. .1..1..0..0..0. .0..1..0..1..1. .0..1..0..1..1
..1..0..0..1..0. .1..1..1..0..0. .0..0..1..1..0. .1..1..0..1..1
..1..1..1..1..1. .0..1..1..1..0. .0..1..1..0..0. .1..1..0..1..1
..0..1..1..0..0. .0..0..1..1..1. .1..1..0..0..0. .0..1..1..0..0
		

Crossrefs

Cf. A297762.

Formula

Empirical recurrence of order 78 (see link above)

A297760 Number of n X 6 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2, 3 or 4 neighboring 1's.

Original entry on oeis.org

1, 225, 4088, 73352, 2263784, 59707529, 1504842706, 39769163381, 1043883771677, 27215281320793, 712187211744833, 18637857993221677, 487388094274625336, 12748605716033435676, 333484777432792798647, 8722865447789945824645
Offset: 1

Views

Author

R. H. Hardin, Jan 05 2018

Keywords

Comments

Column 6 of A297762.

Examples

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

Crossrefs

Cf. A297762.

A297761 Number of nX7 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2, 3 or 4 neighboring 1s.

Original entry on oeis.org

1, 733, 24801, 759243, 45618455, 2301783905, 108229776807, 5394743533114, 267870723932943, 13164280362488109, 649645311987327236, 32083173143952274627, 1582748891993544903545, 78096927219843019316942
Offset: 1

Views

Author

R. H. Hardin, Jan 05 2018

Keywords

Comments

Column 7 of A297762.

Examples

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

Crossrefs

Cf. A297762.

A297763 Number of 2Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2, 3 or 4 neighboring 1s.

Original entry on oeis.org

1, 2, 12, 31, 78, 225, 733, 2305, 7156, 22388, 70737, 223576, 705927, 2229237, 7044181, 22263130, 70360408, 222365159, 702781362, 2221173901, 7020142785, 22187534409, 70124998492, 221634512416, 700490315089, 2213945357924
Offset: 1

Views

Author

R. H. Hardin, Jan 05 2018

Keywords

Comments

Row 2 of A297762.

Examples

			Some solutions for n=7
..0..0..1..1..0..1..1. .0..1..1..1..1..1..0. .0..0..1..1..1..1..1
..0..1..1..0..0..1..1. .0..1..1..0..1..1..1. .0..0..0..1..0..1..1
		

Crossrefs

Cf. A297762.

Formula

Empirical: a(n) = 4*a(n-1) -3*a(n-2) +a(n-3) +6*a(n-4) -18*a(n-5)

A297764 Number of 3 X n 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2, 3 or 4 neighboring 1's.

Original entry on oeis.org

1, 4, 52, 206, 734, 4088, 24801, 130159, 666434, 3560105, 19245643, 102730864, 546125038, 2913904858, 15571288925, 83122383401, 443489006259, 2366877041892, 12634189755271, 67434790018093, 359910312437155, 1920940558913908
Offset: 1

Views

Author

R. H. Hardin, Jan 05 2018

Keywords

Comments

Row 3 of A297762.

Examples

			Some solutions for n=7
..0..0..0..0..1..1..0. .0..1..1..1..1..1..0. .0..0..0..0..1..0..0
..1..1..1..0..1..1..1. .0..1..1..1..1..0..1. .0..0..0..1..1..1..0
..0..1..1..1..1..1..0. .0..0..0..0..0..1..0. .0..0..1..1..1..0..0
		

Crossrefs

Cf. A297762.

Formula

Empirical: a(n) = 6*a(n-1) -5*a(n-2) +8*a(n-3) +53*a(n-4) -295*a(n-5) -76*a(n-6) +556*a(n-7) +178*a(n-8) +196*a(n-9) +145*a(n-10) -779*a(n-11) -628*a(n-12) +226*a(n-13) +100*a(n-14) +275*a(n-15) +152*a(n-16) -65*a(n-17) -32*a(n-18) -26*a(n-19) -4*a(n-20).

A297765 Number of 4Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2, 3 or 4 neighboring 1s.

Original entry on oeis.org

1, 7, 186, 1181, 7081, 73352, 759243, 6588378, 57693478, 533724767, 4922696680, 44623406796, 405152379143, 3698469278671, 33742294413274, 307321953516448, 2799705826422060, 25518781471597350, 232579566114463247
Offset: 1

Views

Author

R. H. Hardin, Jan 05 2018

Keywords

Comments

Row 4 of A297762.

Examples

			Some solutions for n=6
..1..1..1..1..0..0. .1..1..0..0..0..0. .1..1..0..1..1..1. .1..1..1..0..1..0
..0..1..0..0..1..1. .1..1..0..1..1..0. .0..1..1..0..1..0. .0..1..0..1..1..1
..0..1..1..1..1..0. .1..0..0..1..1..1. .1..1..0..0..1..1. .1..1..0..1..0..0
..0..0..1..0..0..0. .0..1..1..1..1..0. .1..1..1..1..1..1. .0..1..1..1..1..0
		

Crossrefs

Cf. A297762.

Formula

Empirical: a(n) = 11*a(n-1) -19*a(n-2) +32*a(n-3) +335*a(n-4) -5302*a(n-5) +4877*a(n-6) +41245*a(n-7) -59158*a(n-8) +30223*a(n-9) +57197*a(n-10) -1020454*a(n-11) +862104*a(n-12) +1838401*a(n-13) -1356530*a(n-14) +2889366*a(n-15) -4139453*a(n-16) -2799504*a(n-17) +1786979*a(n-18) -6970729*a(n-19) -1083380*a(n-20) +15771978*a(n-21) +4518181*a(n-22) +3914585*a(n-23) +906744*a(n-24) -18794319*a(n-25) -6388380*a(n-26) -2837951*a(n-27) +4295886*a(n-28) +8890326*a(n-29) +7281990*a(n-30) +3637924*a(n-31) -6921628*a(n-32) -9675860*a(n-33) -591149*a(n-34) +5705591*a(n-35) +1517078*a(n-36) +690601*a(n-37) -452385*a(n-38) -849043*a(n-39) -331785*a(n-40) -330259*a(n-41) +105500*a(n-42) +119342*a(n-43) -10526*a(n-44) +21152*a(n-45) +4084*a(n-46) -10053*a(n-47) +508*a(n-48) +1494*a(n-49) -228*a(n-50) -132*a(n-51) +4*a(n-52)

A297766 Number of 5Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2, 3 or 4 neighboring 1s.

Original entry on oeis.org

1, 14, 1045, 10639, 109228, 2263784, 45618455, 739821272, 12181204009, 214913229652, 3770723150572, 64742737047855, 1114199103262826, 19305756803013227, 334233068253483784, 5774144936515374280
Offset: 1

Views

Author

R. H. Hardin, Jan 05 2018

Keywords

Comments

Row 5 of A297762.

Examples

			Some solutions for n=5
..1..1..0..0..0. .0..0..0..1..1. .0..1..1..1..0. .0..0..0..1..1
..0..1..1..0..0. .0..0..1..1..1. .0..1..1..1..0. .0..0..0..1..1
..1..0..1..1..0. .1..1..0..1..0. .0..0..1..0..0. .0..1..0..1..0
..0..1..0..1..0. .1..1..0..1..1. .0..1..0..1..0. .1..0..1..0..1
..1..1..1..1..1. .1..1..1..1..0. .0..0..1..0..0. .0..1..0..1..0
		

Crossrefs

Cf. A297762.

A297767 Number of 6Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2, 3 or 4 neighboring 1s.

Original entry on oeis.org

1, 31, 5685, 90727, 1456855, 59707529, 2301783905, 66213677238, 1944129099097, 63049230136397, 2027401928062934, 63102413279467578, 1970605911207789423, 62210056801807436056, 1961461031452058351683, 61622985760713701597898
Offset: 1

Views

Author

R. H. Hardin, Jan 05 2018

Keywords

Comments

Row 6 of A297762.

Examples

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

Crossrefs

Cf. A297762.
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