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.

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A249986 Number of length 6+1 0..2*n arrays with the sum of the absolute values of adjacent differences equal to 6*n.

Original entry on oeis.org

466, 7138, 43068, 168506, 508902, 1290856, 2886016, 5862924, 11046810, 19587334, 33034276, 53421174, 83356910, 126125244, 185792296, 267321976, 376699362, 521062026, 708839308, 949899538, 1255705206, 1639476080, 2116360272
Offset: 1

Views

Author

R. H. Hardin, Nov 10 2014

Keywords

Examples

			Some solutions for n=4:
..5....0....0....5....2....4....2....5....2....0....0....3....0....0....1....5
..2....5....7....0....8....7....4....0....1....1....3....0....2....2....7....1
..0....0....1....6....6....1....0....7....7....6....6....8....7....0....2....5
..8....0....3....8....1....6....6....8....0....8....4....8....1....4....0....2
..0....4....4....8....5....0....0....5....3....2....8....1....3....6....0....5
..2....8....8....0....7....3....5....0....5....6....1....7....6....0....7....8
..3....2....4....3....2....2....4....3....0....0....6....7....0....8....3....1

Links

Crossrefs

Row 6 of A249982.

Formula

Empirical: a(n) = (1987/180)*n^6 + (2033/30)*n^5 + (2785/18)*n^4 + 226*n^3 - (3017/180)*n^2 + (697/30)*n.
Conjectures from Colin Barker, Nov 10 2018: (Start)
G.f.: 2*x*(233 + 1938*x + 1444*x^2 + 309*x^3 + 134*x^4 - 84*x^5) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)

A249987 Number of length 7+1 0..2*n arrays with the sum of the absolute values of adjacent differences equal to 7*n.

Original entry on oeis.org

1012, 31380, 245860, 1293326, 4598532, 14027522, 35380112, 82176822, 170479400, 335836428, 613774848, 1082535196, 1809905436, 2948384694, 4614428112, 7080133636, 10530399420, 15419165316, 22022418940, 31058475666, 42919172164
Offset: 1

Views

Author

R. H. Hardin, Nov 10 2014

Keywords

Comments

Row 7 of A249982

Examples

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

Links

Formula

Empirical: a(n) = 2*a(n-1) +5*a(n-2) -12*a(n-3) -9*a(n-4) +30*a(n-5) +5*a(n-6) -40*a(n-7) +5*a(n-8) +30*a(n-9) -9*a(n-10) -12*a(n-11) +5*a(n-12) +2*a(n-13) -a(n-14)
Empirical for n mod 2 = 0: a(n) = (459901/26880)*n^7 + (238219/1920)*n^6 + (682979/1920)*n^5 + (30971/64)*n^4 + (124069/480)*n^3 + (337/240)*n^2 + (10541/420)*n
Empirical for n mod 2 = 1: a(n) = (459901/26880)*n^7 + (238219/1920)*n^6 + (86757/256)*n^5 + (50735/128)*n^4 + (513337/3840)*n^3 - (25939/1920)*n^2 + (87707/5376)*n - (119/128)
Previous Showing 11-12 of 12 results.

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

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