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.

Previous Showing 11-14 of 14 results.

A241617 Number of length n+2 0..11 arrays with no consecutive three elements summing to more than 11.

Original entry on oeis.org

364, 2366, 15379, 93457, 583089, 3672032, 22925695, 143212290, 896486942, 5607651699, 35066570585, 219346221757, 1372020569832, 8581465964097, 53675165117172, 335729445819781, 2099913330669171, 13134499972175218
Offset: 1

Views

Author

R. H. Hardin, Apr 26 2014

Keywords

Comments

Column 11 of A241619

Examples

			Some solutions for n=5
..6....3....3....0....6....6....6....0....0....3....3....3....6....3....0....3
..0....3....6....0....3....0....0....1....3....0....0....0....0....0....0....0
..4....2....1....6....2....3....0....3....0....7....0....1....4....2....0....1
..5....2....2....0....5....0....7....0....4....3...11....1....6....1....4....4
..2....1....5....1....4....2....3....6....0....1....0....7....0....1....3....5
..0....0....3....4....0....4....0....3....7....4....0....0....5....4....0....2
..9....2....1....6....2....1....4....2....2....5....2....4....2....6....0....0

Links

Formula

Empirical recurrence of order 78 (see link above)

A241620 Number of length 5+2 0..n arrays with no consecutive three elements summing to more than n.

Original entry on oeis.org

19, 147, 711, 2567, 7586, 19374, 44274, 92697, 180829, 332761, 583089, 980031, 1589108, 2497436, 3818676, 5698689, 8321943, 11918719, 16773163, 23232231, 31715574, 42726410, 56863430, 74833785, 97467201, 125731269, 160747957
Offset: 1

Views

Author

R. H. Hardin, Apr 26 2014

Keywords

Examples

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

Links

Crossrefs

Row 5 of A241619.

Formula

Empirical: a(n) = (47/5040)*n^7 + (47/360)*n^6 + (7/9)*n^5 + (23/9)*n^4 + (3599/720)*n^3 + (2093/360)*n^2 + (26/7)*n + 1.
Conjectures from Colin Barker, Oct 30 2018: (Start)
G.f.: x*(19 - 5*x + 67*x^2 - 69*x^3 + 56*x^4 - 28*x^5 + 8*x^6 - x^7) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
(End)

A241621 Number of length 6+2 0..n arrays with no consecutive three elements summing to more than n.

Original entry on oeis.org

28, 287, 1730, 7483, 25774, 75180, 193194, 449295, 963886, 1934647, 3672032, 6645821, 11544820, 19351984, 31437420, 49671909, 76563768, 115422055, 170549302, 247467143, 353178386, 496469260, 688255750, 941978115, 1274047866
Offset: 1

Views

Author

R. H. Hardin, Apr 26 2014

Keywords

Examples

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

Links

Crossrefs

Row 6 of A241619.

Formula

Empirical: a(n) = (13/2880)*n^8 + (13/180)*n^7 + (145/288)*n^6 + (719/360)*n^5 + (14197/2880)*n^4 + (2789/360)*n^3 + (121/16)*n^2 + (251/60)*n + 1.
Conjectures from Colin Barker, Oct 30 2018: (Start)
G.f.: x*(28 + 35*x + 155*x^2 - 107*x^3 + 127*x^4 - 84*x^5 + 36*x^6 - 9*x^7 + x^8) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
(End)

A241622 Number of length 7+2 0..n arrays with no consecutive three elements summing to more than n.

Original entry on oeis.org

41, 556, 4175, 21631, 86828, 289248, 835812, 2159025, 5093737, 11151140, 22925695, 44678543, 83149600, 148659968, 256576512, 429221457, 698321649, 1108104700, 1719162599, 2613217519, 3898939484, 5718981280, 8258412500, 11754751905
Offset: 1

Views

Author

R. H. Hardin, Apr 26 2014

Keywords

Examples

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

Links

Crossrefs

Row 7 of A241619.

Formula

Empirical: a(n) = (131/60480)*n^9 + (131/3360)*n^8 + (3137/10080)*n^7 + (347/240)*n^6 + (12407/2880)*n^5 + (4097/480)*n^4 + (169957/15120)*n^3 + (7963/840)*n^2 + (487/105)*n + 1.
Conjectures from Colin Barker, Oct 30 2018: (Start)
G.f.: x*(41 + 146*x + 460*x^2 - 19*x^3 + 283*x^4 - 209*x^5 + 120*x^6 - 45*x^7 + 10*x^8 - x^9) / (1 - x)^10.
a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.
(End)
Previous Showing 11-14 of 14 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.