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

A249461 Number of length n+4 0..3 arrays with no five consecutive terms having four times any element equal to the sum of the remaining four.

Original entry on oeis.org

860, 2948, 10124, 34832, 119932, 412972, 1422232, 4898776, 16874830, 58131580, 200257200, 689871586, 2376578686, 8187255382, 28204984386, 97165888404, 334735779168, 1153163060226, 3972642458048, 13685741942400, 47147347303294
Offset: 1

Views

Author

R. H. Hardin, Oct 29 2014

Keywords

Comments

Column 3 of A249466

Examples

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

Links

A249462 Number of length n+4 0..4 arrays with no five consecutive terms having four times any element equal to the sum of the remaining four.

Original entry on oeis.org

2640, 11260, 48180, 206428, 884728, 3791504, 16249428, 69646680, 298527530, 1279613894, 5484967770, 23510991158, 100778855292, 431985293958, 1851693204500, 7937234390598, 34022755120144, 145837709303458
Offset: 1

Views

Author

R. H. Hardin, Oct 29 2014

Keywords

Comments

Column 4 of A249466.

Examples

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

Links

Crossrefs

Cf. A249466.

A249463 Number of length n+4 0..5 arrays with no five consecutive terms having four times any element equal to the sum of the remaining four.

Original entry on oeis.org

6730, 35322, 185982, 980718, 5174842, 27309702, 144140836, 760833398, 4016197550, 21200828116, 111916666626, 590797789556, 3118776430716, 16463816131498, 86911505863698, 458800889433320, 2421984333500072
Offset: 1

Views

Author

R. H. Hardin, Oct 29 2014

Keywords

Comments

Column 5 of A249466

Examples

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

Links

A249464 Number of length n+4 0..6 arrays with no five consecutive terms having four times any element equal to the sum of the remaining four.

Original entry on oeis.org

14730, 91160, 565516, 3512232, 21824440, 135637752, 843025344, 5239822940, 32568952752, 202440565098, 1258327314766, 7821507915080, 48616960819938, 302193724046726, 1878379190428402, 11675652828179748, 72573673473580502
Offset: 1

Views

Author

R. H. Hardin, Oct 29 2014

Keywords

Comments

Column 6 of A249466

Examples

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

Links

A249465 Number of length n+4 0..7 arrays with no five consecutive terms having four times any element equal to the sum of the remaining four.

Original entry on oeis.org

29060, 207760, 1488294, 10671554, 76550058, 549183692, 3940066010, 28268238072, 202814997034, 1455140474848, 10440249554448, 74906102995968, 537432238422096, 3855940687831096, 27665406008609022, 198492352203114492
Offset: 1

Views

Author

R. H. Hardin, Oct 29 2014

Keywords

Comments

Column 7 of A249466

Examples

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

Links

A249467 Number of length 1+4 0..n arrays with no five consecutive terms having four times any element equal to the sum of the remaining four.

Original entry on oeis.org

30, 190, 860, 2640, 6730, 14730, 29060, 52900, 90390, 146610, 228000, 342120, 498030, 706270, 979100, 1330440, 1776250, 2334330, 3024740, 3869740, 4893990, 6124530, 7591200, 9326400, 11365470, 13746670, 16511420, 19704240, 23373130
Offset: 1

Views

Author

R. H. Hardin, Oct 29 2014

Keywords

Examples

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

Links

Crossrefs

Row 1 of A249466.

Formula

Empirical: a(n) = 4*a(n-1) - 6*a(n-2) + 5*a(n-3) - 4*a(n-4) + 2*a(n-5) + 2*a(n-6) - 4*a(n-7) + 5*a(n-8) - 6*a(n-9) + 4*a(n-10) - a(n-11).
Also a polynomial of degree 5 plus a constant pseudonomial with period 12:
Empirical for n mod 12 = 0: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n
Empirical for n mod 12 = 1: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n + (65/12)
Empirical for n mod 12 = 2: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n - (20/3)
Empirical for n mod 12 = 3: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n + (35/4)
Empirical for n mod 12 = 4: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n - (40/3)
Empirical for n mod 12 = 5: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n + (145/12)
Empirical for n mod 12 = 6: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n
Empirical for n mod 12 = 7: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n - (55/12)
Empirical for n mod 12 = 8: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n - (20/3)
Empirical for n mod 12 = 9: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n + (75/4)
Empirical for n mod 12 = 10: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n - (40/3)
Empirical for n mod 12 = 11: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n + (25/12).
Empirical g.f.: 10*x*(3 + 7*x + 28*x^2 + 19*x^3 + 50*x^4 + 5*x^5 + 32*x^6 - 3*x^7 + 3*x^8) / ((1 - x)^6*(1 + x)*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Nov 09 2018

A249468 Number of length 2+4 0..n arrays with no five consecutive terms having four times any element equal to the sum of the remaining four.

Original entry on oeis.org

58, 464, 2948, 11260, 35322, 91160, 207760, 429364, 821614, 1475648, 2518348, 4114408, 6479030, 9883248, 14668588, 21247164, 30124654, 41900528, 57290148, 77134712, 102409834, 134241312, 173931480, 222958784, 283011294, 355982968
Offset: 1

Views

Author

R. H. Hardin, Oct 29 2014

Keywords

Comments

Row 2 of A249466

Examples

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

Links

A249469 Number of length 3+4 0..n arrays with no five consecutive terms having four times any element equal to the sum of the remaining four.

Original entry on oeis.org

112, 1140, 10124, 48180, 185982, 565516, 1488294, 3491108, 7479834, 14872588, 27848932, 49534034, 84370308, 138424022, 219934350, 339564798, 511246534, 752562638, 1085714794, 1538310894, 2144026442, 2943704164, 3986818718
Offset: 1

Views

Author

R. H. Hardin, Oct 29 2014

Keywords

Comments

Row 3 of A249466

Examples

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

Links

A249470 Number of length 4+4 0..n arrays with no five consecutive terms having four times any element equal to the sum of the remaining four.

Original entry on oeis.org

216, 2802, 34832, 206428, 980718, 3512232, 10671554, 28408106, 68141702, 149985134, 308128976, 596635030, 1099154100, 1939520516, 3298783802, 5428583306, 8678985766, 13520275360, 20580791722, 30686017266, 44896600642
Offset: 1

Views

Author

R. H. Hardin, Oct 29 2014

Keywords

Comments

Row 4 of A249466

Examples

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

Links

A249471 Number of length 5+4 0..n arrays with no five consecutive terms having four times any element equal to the sum of the remaining four.

Original entry on oeis.org

416, 6872, 119932, 884728, 5174842, 21824440, 76550058, 231236220, 620927172, 1512868480, 3409871172, 7187658694, 14321688284, 27179247012, 49484565130, 86796151488, 147351090962, 242923972126, 390163791394, 612170875944
Offset: 1

Views

Author

R. H. Hardin, Oct 29 2014

Keywords

Comments

Row 5 of A249466

Examples

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

Links

Showing 1-10 of 12 results. Next

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