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 1-7 of 7 results.

A242542 Number of length n+3 0..n arrays with no four elements in a row with pattern aabb (possibly a=b) and new values 0..n introduced in 0..n order.

Original entry on oeis.org

6, 32, 150, 690, 3311, 16968, 93103, 544920, 3386262, 22243902, 153850981, 1116625523, 8478969009, 67185160511, 554235206898, 4750165417926, 42219358673456, 388485398829204, 3695187060252009, 36282147267628868
Offset: 1

Views

Author

R. H. Hardin, May 17 2014

Keywords

Comments

Diagonal of A242549

Examples

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

Links

A242543 Number of length n+3 0..2 arrays with no four elements in a row with pattern aabb (possibly a=b) and new values 0..2 introduced in 0..2 order.

Original entry on oeis.org

12, 32, 88, 242, 660, 1800, 4920, 13448, 36736, 100352, 274176, 749088, 2046528, 5591168, 15275392, 41733248, 114017280, 311500800, 851036160, 2325074432, 6352221184, 17354590208, 47413622784, 129536428032, 353900101632
Offset: 1

Views

Author

R. H. Hardin, May 17 2014

Keywords

Comments

Column 2 of A242549

Examples

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

Links

Formula

Empirical: a(n) = 2*a(n-1) +4*a(n-3) +4*a(n-4).
Empirical: G.f.: -2*x*(6+4*x+12*x^2+9*x^3) / ( (2*x^2+2*x-1)*(2*x^2+1) ). - R. J. Mathar, May 18 2014

A242544 Number of length n+3 0..3 arrays with no four elements in a row with pattern aabb (possibly a=b) and new values 0..3 introduced in 0..3 order.

Original entry on oeis.org

13, 42, 150, 554, 2072, 7808, 29536, 111878, 423969, 1607058, 6092367, 23097242, 87566957, 331989206, 1258663594, 4771951574, 18091832688, 68591328768, 260049450816, 985922294306, 3737915147525, 14171512153838, 53728281674119
Offset: 1

Views

Author

R. H. Hardin, May 17 2014

Keywords

Comments

Column 3 of A242549

Examples

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

Links

Formula

Empirical: a(n) = 4*a(n-1) -3*a(n-2) +10*a(n-3) -2*a(n-4) -12*a(n-5) -9*a(n-6) -18*a(n-7) -9*a(n-8).
Empirical: G.f.: -x*(-13+10*x-21*x^2+50*x^3+88*x^4+78*x^5+99*x^6+42*x^7) / ( (x^2+x-1)*(3*x^2+3*x-1)*(3*x^2+1)*(x^2+1) ). - R. J. Mathar, May 18 2014

A242545 Number of length n+3 0..4 arrays with no four elements in a row with pattern aabb (possibly a=b) and new values 0..4 introduced in 0..4 order.

Original entry on oeis.org

13, 43, 165, 690, 3050, 13988, 65588, 311431, 1489435, 7152787, 34431086, 165959996, 800539194, 3863197403, 18647303797, 90021133115, 434616726192, 2098395654912, 10131623972784, 48918915963483, 236198983546635
Offset: 1

Views

Author

R. H. Hardin, May 17 2014

Keywords

Comments

Column 4 of A242549.

Examples

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

Links

Crossrefs

Cf. A242549.

Formula

Empirical: a(n) = 7*a(n-1) -14*a(n-2) +29*a(n-3) -53*a(n-4) -18*a(n-5) -28*a(n-6) -56*a(n-7) +140*a(n-8) +176*a(n-9) +192*a(n-10) +192*a(n-11) +64*a(n-12).
Empirical: G.f.: -x*(13 -48*x +46*x^2 -240*x^3 -28*x^4 +26*x^5 +245*x^6 +1169*x^7 +1276*x^8 +1240*x^9 +992*x^10 +296*x^11) / ( (2*x^2+2*x-1) *(x^2+x-1) *(2*x^2+1) *(x^2+1) *(4*x^2+1) *(4*x^2+4*x-1) ). - R. J. Mathar, May 18 2014

A242546 Number of length n+3 0..5 arrays with no four elements in a row with pattern aabb (possibly a=b) and new values 0..5 introduced in 0..5 order.

Original entry on oeis.org

13, 43, 166, 711, 3311, 16512, 86671, 471698, 2631790, 14930915, 85644696, 494803149, 2872024482, 16720674459, 97536295951, 569673328615, 3329960486206, 19475149500576, 113938441220822, 666738150322630, 3902133809773705
Offset: 1

Views

Author

R. H. Hardin, May 17 2014

Keywords

Comments

Column 5 of A242549

Examples

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

Links

Formula

Empirical: a(n) = 11*a(n-1) -41*a(n-2) +100*a(n-3) -259*a(n-4) +283*a(n-5) -178*a(n-6) +383*a(n-7) +1393*a(n-8) +312*a(n-9) +723*a(n-10) -1707*a(n-11) -5129*a(n-12) -5430*a(n-13) -5400*a(n-14) -3600*a(n-15) -900*a(n-16)

A242547 Number of length n+3 0..6 arrays with no four elements in a row with pattern aabb (possibly a=b) and new values 0..6 introduced in 0..6 order.

Original entry on oeis.org

13, 43, 166, 712, 3339, 16968, 92360, 532175, 3210136, 20066475, 128848615, 843831762, 5605476437, 37615886287, 254237240993, 1726996739311, 11772647808288, 80450209850112, 550717024856208, 3774443585348691
Offset: 1

Views

Author

R. H. Hardin, May 17 2014

Keywords

Comments

Column 6 of A242549

Examples

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

Links

Formula

Empirical: a(n) = 16*a(n-1) -95*a(n-2) +326*a(n-3) -998*a(n-4) +2268*a(n-5) -2953*a(n-6) +5002*a(n-7) -877*a(n-8) -8932*a(n-9) -5460*a(n-10) -46536*a(n-11) -36728*a(n-12) -4608*a(n-13) +43488*a(n-14) +180288*a(n-15) +260208*a(n-16) +254016*a(n-17) +207360*a(n-18) +103680*a(n-19) +20736*a(n-20)

A242548 Number of length n+3 0..7 arrays with no four elements in a row with pattern aabb (possibly a=b) and new values 0..7 introduced in 0..7 order.

Original entry on oeis.org

13, 43, 166, 712, 3340, 17004, 93103, 543773, 3362689, 21854355, 148145552, 1039764960, 7504319914, 55361803579, 415379230159, 3156808241415, 24223346602916, 187213792659552, 1454634743756302, 11346966341306231
Offset: 1

Views

Author

R. H. Hardin, May 17 2014

Keywords

Comments

Column 7 of A242549

Examples

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

Links

Formula

Empirical: a(n) = 22*a(n-1) -190*a(n-2) +924*a(n-3) -3465*a(n-4) +10962*a(n-5) -24402*a(n-6) +45828*a(n-7) -74016*a(n-8) +19016*a(n-9) -23090*a(n-10) -159064*a(n-11) +571211*a(n-12) +704098*a(n-13) +1846562*a(n-14) +2774132*a(n-15) +616507*a(n-16) -2599138*a(n-17) -8906720*a(n-18) -16117180*a(n-19) -18096476*a(n-20) -15823920*a(n-21) -10584000*a(n-22) -4233600*a(n-23) -705600*a(n-24)
Showing 1-7 of 7 results.

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

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