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

A250321 Number of length 2+2 0..n arrays with the sum of second differences squared multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

8, 25, 60, 117, 200, 321, 480, 681, 940, 1253, 1624, 2073, 2592, 3185, 3876, 4653, 5520, 6505, 7592, 8785, 10116, 11565, 13136, 14865, 16728, 18729, 20908, 23237, 25720, 28401, 31248, 34265, 37500, 40917, 44520, 48361, 52400, 56641, 61140, 65853, 70784
Offset: 1

Views

Author

R. H. Hardin, Nov 18 2014

Keywords

Comments

Row 2 of A250320.

Examples

			Some solutions for n=6:
..2....5....6....1....4....1....6....3....3....2....6....0....3....1....0....0
..2....6....1....0....1....3....5....4....4....1....1....0....0....4....3....4
..0....0....6....1....6....3....3....3....0....2....1....2....6....3....1....1
..0....1....1....4....3....5....0....0....1....5....6....6....3....6....4....5

Links

Crossrefs

Cf. A250320.

Formula

Empirical: a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) - 4*a(n-4) + 2*a(n-5) - a(n-6) + 2*a(n-7) - a(n-8).
Empirical g.f.: x*(8 + 9*x + 18*x^2 + 6*x^3 + 8*x^4 + 2*x^5 + 2*x^6 - x^7) / ((1 - x)^4*(1 + x + x^2)^2). - Colin Barker, Mar 19 2018

A250313 Number of length n+2 0..1 arrays with the sum of second differences squared multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

2, 8, 8, 24, 42, 104, 212, 464, 950, 1968, 3984, 8072, 16226, 32600, 65324, 130848, 261870, 524000, 1048232, 2096792, 4193882, 8388168, 16776708, 33553904, 67108262, 134217104, 268434752, 536870184, 1073741010, 2147482808, 4294966364
Offset: 1

Views

Author

R. H. Hardin, Nov 18 2014

Keywords

Examples

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

Links

Crossrefs

Column 1 of A250320.

Formula

Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 3*a(n-4) + 3*a(n-5) - 2*a(n-6).
Empirical g.f.: 2*x*(1 + x - 8*x^2 + 6*x^3 + 6*x^4 - 2*x^5) / ((1 - x)^3*(1 + x)^2*(1 - 2*x)). - Colin Barker, Nov 12 2018

A250314 Number of length n+2 0..2 arrays with the sum of second differences squared multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

5, 25, 41, 161, 487, 1689, 5849, 19981, 67459, 221953, 709677, 2225181, 6874957, 21019457, 63845081, 193077349, 582247055, 1752693185, 5269930487, 15833493125, 47548549519, 142743601321, 428431672069, 1285708580949, 3857979555851
Offset: 1

Views

Author

R. H. Hardin, Nov 18 2014

Keywords

Comments

Column 2 of A250320

Examples

			Some solutions for n=6
..2....1....1....2....0....1....0....2....1....1....1....0....0....0....1....1
..2....0....0....2....1....0....2....1....1....0....1....1....0....2....0....1
..1....0....0....0....1....0....2....1....1....0....2....0....1....1....0....1
..0....0....0....1....2....1....1....2....1....1....2....2....1....1....0....1
..1....0....2....1....1....0....0....1....1....2....1....0....2....2....0....2
..2....1....0....2....1....2....1....1....1....2....0....0....2....1....0....0
..2....1....1....0....1....2....1....1....0....2....1....0....0....2....1....0
..0....0....0....2....0....1....1....2....0....1....1....1....0....2....2....2

Links

A250322 Number of length 3+2 0..n arrays with the sum of second differences squared multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

8, 41, 104, 233, 436, 745, 1152, 1733, 2460, 3441, 4612, 6073, 7752, 9789, 12108, 14837, 17916, 21489, 25444, 30013, 34996, 40621, 46736, 53569, 60892, 68973, 77660, 87237, 97468, 108653, 120596, 133561, 147300, 162157, 177824, 194673, 212388
Offset: 1

Views

Author

R. H. Hardin, Nov 18 2014

Keywords

Comments

Row 3 of A250320

Examples

			Some solutions for n=6
..6....5....6....2....3....0....4....3....1....2....1....1....0....6....1....2
..1....5....0....0....6....3....1....6....2....3....1....1....3....4....3....3
..3....5....3....2....3....6....1....6....2....4....1....5....4....5....5....4
..5....0....6....1....0....5....1....6....3....3....4....4....5....6....0....0
..0....0....0....5....3....0....4....3....4....0....4....6....4....4....2....1

Links

A250315 Number of length n+2 0..3 arrays with the sum of second differences squared multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

8, 60, 104, 652, 2432, 12820, 61092, 300616, 1423966, 6523576, 28749998, 122577404, 509838050, 2086581780, 8455716678, 34069235524
Offset: 1

Views

Author

R. H. Hardin, Nov 18 2014

Keywords

Comments

Column 3 of A250320

Examples

			Some solutions for n=6
..0....0....0....0....1....3....0....0....2....2....2....2....1....0....3....1
..1....1....2....2....0....2....3....1....3....1....3....0....2....0....0....3
..1....1....3....0....3....0....3....0....2....3....3....0....0....2....0....3
..0....3....1....2....2....1....3....0....2....3....1....1....0....2....0....0
..2....3....0....1....2....3....3....1....1....3....1....0....1....2....2....2
..0....2....3....3....3....3....1....3....3....1....1....0....3....0....2....2
..1....1....3....1....3....0....0....2....3....2....1....1....1....2....2....0
..2....0....3....3....2....1....1....3....0....3....2....1....2....2....1....0

A250316 Number of length n+2 0..4 arrays with the sum of second differences squared multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

13, 117, 233, 1773, 8767, 57833, 363457, 2317841, 14305925, 85334033, 487200669, 2669191565, 14140938607
Offset: 1

Views

Author

R. H. Hardin, Nov 18 2014

Keywords

Comments

Column 4 of A250320

Examples

			Some solutions for n=6
..4....3....2....2....2....3....4....2....2....3....1....3....3....3....3....3
..0....1....3....2....3....2....0....0....0....1....3....2....4....0....2....4
..1....0....0....4....4....0....0....3....3....3....4....1....1....0....0....0
..4....3....0....2....3....4....3....2....1....4....3....1....0....1....4....1
..2....4....3....3....4....3....3....2....1....2....3....3....1....1....3....0
..4....4....2....4....3....1....4....4....4....3....4....3....1....3....0....4
..0....2....2....0....2....3....4....4....4....4....2....0....4....2....1....3
..0....4....1....2....3....0....4....4....2....4....4....1....3....3....2....4

A250317 Number of length n+2 0..5 arrays with the sum of second differences squared multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

18, 200, 436, 3916, 24126, 197848, 1559080, 12424332, 95711098, 709795516, 5002719434, 33563203028
Offset: 1

Views

Author

R. H. Hardin, Nov 18 2014

Keywords

Comments

Column 5 of A250320

Examples

			Some solutions for n=6
..2....0....1....1....3....4....1....2....3....3....1....5....1....1....0....0
..3....3....1....1....3....0....0....0....0....0....1....3....1....0....0....4
..2....3....3....0....2....4....4....4....1....2....1....3....0....2....4....3
..3....5....1....3....4....2....5....5....5....3....3....0....3....5....4....4
..1....0....5....3....3....2....0....0....4....1....1....2....5....3....0....3
..1....1....5....1....0....3....0....1....2....3....2....0....4....4....4....5
..2....4....2....1....0....1....2....4....0....4....5....0....3....3....5....2
..1....5....2....5....2....3....3....0....5....5....3....0....5....0....1....2

A250318 Number of length n+2 0..6 arrays with the sum of second differences squared multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

25, 321, 745, 7969, 57305, 558541, 5237161, 50020061, 461868677, 4110975765
Offset: 1

Views

Author

R. H. Hardin, Nov 18 2014

Keywords

Comments

Column 6 of A250320

Examples

			Some solutions for n=5
..1....3....6....4....0....6....0....1....5....6....2....2....2....2....3....5
..3....3....1....0....1....5....6....0....6....5....1....5....2....5....3....4
..6....1....1....1....4....2....3....4....4....2....2....3....2....4....2....0
..6....2....5....5....5....1....1....4....5....6....3....4....6....4....4....3
..4....4....6....6....2....1....6....6....5....5....2....1....6....6....0....1
..6....6....6....3....3....5....4....5....4....2....0....5....2....5....1....3
..6....6....5....3....4....6....6....6....3....3....1....0....2....2....3....4

A250319 Number of length n+2 0..7 arrays with the sum of second differences squared multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

32, 480, 1152, 14452, 119004, 1357424, 14866258, 166783380, 1809575752
Offset: 1

Views

Author

R. H. Hardin, Nov 18 2014

Keywords

Comments

Column 7 of A250320

Examples

			Some solutions for n=5
..6....3....2....3....2....7....6....0....1....5....0....4....7....3....3....6
..4....3....6....3....2....6....7....4....1....2....5....1....3....3....7....2
..3....6....4....2....5....6....5....3....2....2....1....3....1....3....0....5
..2....0....4....2....3....7....4....4....0....0....6....0....2....2....5....1
..2....3....0....4....4....7....7....6....6....0....6....2....1....5....6....5
..1....1....7....6....2....5....7....4....3....4....2....0....1....4....4....0
..1....3....1....6....4....2....6....4....3....7....1....1....5....4....6....4

A250323 Number of length 4+2 0..n arrays with the sum of second differences squared multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

24, 161, 652, 1773, 3916, 7969, 14452, 24293, 38720, 59201, 86768, 123737, 170864, 231061, 307156, 400573, 512768, 650369, 812560, 1003945, 1228880, 1491229, 1791156, 2138429, 2532856, 2981513, 3489820, 4060069, 4693008
Offset: 1

Views

Author

R. H. Hardin, Nov 18 2014

Keywords

Comments

Row 4 of A250320

Examples

			Some solutions for n=6
..2....2....2....1....1....4....1....2....4....2....0....3....3....1....2....2
..0....3....2....3....4....4....2....0....3....5....1....0....4....4....0....4
..1....4....6....4....4....1....2....3....4....6....1....1....4....3....0....5
..3....0....6....4....5....5....0....1....4....4....4....6....5....1....3....3
..2....1....4....3....3....0....0....2....2....3....4....6....1....3....3....2
..2....2....0....1....0....6....1....0....3....0....5....1....2....4....1....4
Showing 1-10 of 13 results. Next

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