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 11 results. Next

A275032 Number of nX3 0..2 arrays with no element equal to any value at offset (0,-1) (-1,-2) or (-2,0) and new values introduced in order 0..2.

Original entry on oeis.org

2, 16, 46, 146, 450, 1428, 4463, 14086, 44195, 139130, 437175, 1375142, 4323125, 13594852, 42745150, 134409630, 422629291, 1328908089, 4178573479, 13138981872, 41313830121, 129905918777, 408472374963, 1284387955519, 4038591382924
Offset: 1

Views

Author

R. H. Hardin, Jul 14 2016

Keywords

Comments

Column 3 of A275037.

Examples

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

Crossrefs

Cf. A275037.

Formula

Empirical: a(n) = 3*a(n-1) +6*a(n-2) -20*a(n-3) -2*a(n-4) +46*a(n-5) -42*a(n-6) -31*a(n-7) +70*a(n-8) -5*a(n-9) -30*a(n-10) -2*a(n-11) +8*a(n-12) +5*a(n-13) -3*a(n-14) -2*a(n-15) +a(n-16) for n>17

A275033 Number of nX4 0..2 arrays with no element equal to any value at offset (0,-1) (-1,-2) or (-2,0) and new values introduced in order 0..2.

Original entry on oeis.org

4, 48, 137, 570, 2334, 9774, 40572, 169348, 704704, 2937764, 12236817, 50996499, 212474695, 885374358, 3689111563, 15371973010, 64051973628, 266893366673, 1112095776824, 4633902454111, 19308634583221, 80455590398414
Offset: 1

Views

Author

R. H. Hardin, Jul 14 2016

Keywords

Comments

Column 4 of A275037.

Examples

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

Crossrefs

Cf. A275037.

Formula

Empirical: a(n) = 4*a(n-1) +14*a(n-2) -62*a(n-3) -40*a(n-4) +388*a(n-5) -306*a(n-6) -1193*a(n-7) +2504*a(n-8) +1764*a(n-9) -7620*a(n-10) -1306*a(n-11) +13370*a(n-12) +1805*a(n-13) -16980*a(n-14) -5291*a(n-15) +18277*a(n-16) +10135*a(n-17) -18477*a(n-18) -12333*a(n-19) +18384*a(n-20) +9126*a(n-21) -15323*a(n-22) -4234*a(n-23) +9693*a(n-24) +1188*a(n-25) -4598*a(n-26) -61*a(n-27) +1605*a(n-28) -135*a(n-29) -382*a(n-30) +68*a(n-31) +53*a(n-32) -14*a(n-33) -3*a(n-34) +a(n-35) for n>37

A275034 Number of nX5 0..2 arrays with no element equal to any value at offset (0,-1) (-1,-2) or (-2,0) and new values introduced in order 0..2.

Original entry on oeis.org

8, 144, 401, 2185, 11624, 64045, 351197, 1931619, 10581148, 58059378, 318560731, 1748917949, 9599252329, 52687857322, 289177064605, 1587227410761, 8711951100374, 47818210862037, 262463115597687, 1440600501570000
Offset: 1

Views

Author

R. H. Hardin, Jul 14 2016

Keywords

Comments

Column 5 of A275037.

Examples

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

Crossrefs

Cf. A275037.

Formula

Empirical recurrence of order 70 (see link above)

A275035 Number of nX6 0..2 arrays with no element equal to any value at offset (0,-1) (-1,-2) or (-2,0) and new values introduced in order 0..2.

Original entry on oeis.org

16, 432, 1152, 8273, 57984, 421793, 3056856, 22207559, 160767947, 1166126087, 8461160013, 61425788827, 445787882372, 3235147655180, 23477974651336, 170398268043384, 1236726092295065, 8975919178977093, 65144744923024289
Offset: 1

Views

Author

R. H. Hardin, Jul 14 2016

Keywords

Comments

Column 6 of A275037.

Examples

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

Crossrefs

Cf. A275037.

A275036 Number of nX7 0..2 arrays with no element equal to any value at offset (0,-1) (-1,-2) or (-2,0) and new values introduced in order 0..2.

Original entry on oeis.org

32, 1296, 3336, 31495, 290927, 2788663, 26631796, 255796423, 2451632155, 23548292980, 226106157788, 2171965131197, 20860224910704, 200378203063185, 1924835061806021, 18490921588045973, 177631680731302175
Offset: 1

Views

Author

R. H. Hardin, Jul 14 2016

Keywords

Comments

Column 7 of A275037.

Examples

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

Crossrefs

Cf. A275037.

A275038 Number of 3 X n 0..2 arrays with no element equal to any value at offset (0,-1) (-1,-2) or (-2,0) and new values introduced in order 0..2.

Original entry on oeis.org

3, 18, 46, 137, 401, 1152, 3336, 9720, 28277, 82174, 238829, 694135, 2017380, 5863430, 17042197, 49533046, 143966504, 418434888, 1216170841, 3534771986, 10273734201, 29860375290, 86788495974, 252248762928, 733155217213
Offset: 1

Views

Author

R. H. Hardin, Jul 14 2016

Keywords

Examples

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

Crossrefs

Row 3 of A275037.

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) + 4*a(n-3) + a(n-4) + 3*a(n-5) + 8*a(n-6) + a(n-7) - 3*a(n-8) - a(n-9) for n>10.
Empirical g.f.: x*(3 + 9*x - 2*x^2 + 23*x^3 + 7*x^4 + 12*x^5 + 10*x^6 - 10*x^7 - 8*x^8 - x^9) / (1 - 3*x + 2*x^2 - 4*x^3 - x^4 - 3*x^5 - 8*x^6 - x^7 + 3*x^8 + x^9). - Colin Barker, Jan 31 2019

A275039 Number of 4Xn 0..2 arrays with no element equal to any value at offset (0,-1) (-1,-2) or (-2,0) and new values introduced in order 0..2.

Original entry on oeis.org

6, 54, 146, 570, 2185, 8273, 31495, 120845, 462819, 1770014, 6774047, 25932054, 99241078, 379774913, 1453487054, 5562892365, 21289984945, 81479806330, 311837664172, 1193456060092, 4567548672431, 17480762283012, 66901812670647
Offset: 1

Views

Author

R. H. Hardin, Jul 14 2016

Keywords

Comments

Row 4 of A275037.

Examples

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

Crossrefs

Cf. A275037.

Formula

Empirical: a(n) = 5*a(n-1) -9*a(n-2) +19*a(n-3) -9*a(n-4) -9*a(n-5) +87*a(n-6) -46*a(n-7) -84*a(n-8) +7*a(n-9) -59*a(n-10) -45*a(n-11) +31*a(n-12) +23*a(n-13) +4*a(n-14) -a(n-15) -a(n-16) +a(n-17) for n>19

A275040 Number of 5Xn 0..2 arrays with no element equal to any value at offset (0,-1) (-1,-2) or (-2,0) and new values introduced in order 0..2.

Original entry on oeis.org

12, 162, 450, 2334, 11624, 57984, 290927, 1465435, 7376949, 37148115, 187150874, 943024281, 4751935274, 23946771826, 120679612086, 608149528211, 3064647978801, 15443791732842, 77826897454970, 392197493948848
Offset: 1

Views

Author

R. H. Hardin, Jul 14 2016

Keywords

Comments

Row 5 of A275037.

Examples

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

Crossrefs

Cf. A275037.

Formula

Empirical: a(n) = 8*a(n-1) -27*a(n-2) +79*a(n-3) -99*a(n-4) -81*a(n-5) +860*a(n-6) -1162*a(n-7) -868*a(n-8) +1676*a(n-9) -3352*a(n-10) -1549*a(n-11) +4857*a(n-12) +1164*a(n-13) +3213*a(n-14) +5946*a(n-15) -1377*a(n-16) -5652*a(n-17) -4880*a(n-18) -2760*a(n-19) -710*a(n-20) +595*a(n-21) +1142*a(n-22) +594*a(n-23) +71*a(n-24) +48*a(n-25) +20*a(n-26) +a(n-28) for n>32

A275041 Number of 6Xn 0..2 arrays with no element equal to any value at offset (0,-1) (-1,-2) or (-2,0) and new values introduced in order 0..2.

Original entry on oeis.org

24, 486, 1428, 9774, 64045, 421793, 2788663, 18527905, 123270618, 820404834, 5457383302, 36311630844, 241731826979, 1609452326761, 10715001495226, 71339194326992, 475007005017394, 3162779499787860, 21058326900918297
Offset: 1

Views

Author

R. H. Hardin, Jul 14 2016

Keywords

Comments

Row 6 of A275037.

Examples

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

Crossrefs

Cf. A275037.

Formula

Empirical recurrence of order 67 (see link above)

A275042 Number of 7Xn 0..2 arrays with no element equal to any value at offset (0,-1) (-1,-2) or (-2,0) and new values introduced in order 0..2.

Original entry on oeis.org

48, 1458, 4463, 40572, 351197, 3056856, 26631796, 233894638, 2060522620, 18133339314, 159409773544, 1403470741331, 12369772366128, 108977203894120, 959787320624928, 8456446218440229, 74528469200536291, 656752270728416591
Offset: 1

Views

Author

R. H. Hardin, Jul 14 2016

Keywords

Comments

Row 7 of A275037.

Examples

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

Crossrefs

Cf. A275037.
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