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

A202956 Number of arrays of n+2 integers in -2..2 with sum zero and adjacent elements differing in absolute value.

Original entry on oeis.org

6, 28, 82, 200, 524, 1724, 5908, 18340, 53680, 162080, 515626, 1651124, 5168256, 15997588, 50018962, 158377344, 502147864, 1584312736, 4991421852, 15779264936, 50053153920, 158866891408, 503893624892, 1598691706648, 5078888702164
Offset: 1

Views

Author

R. H. Hardin, Dec 26 2011

Keywords

Comments

Column 2 of A202962.

Examples

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

Links

Crossrefs

Cf. A202962.

A202957 Number of arrays of n+2 integers in -3..3 with sum zero and adjacent elements differing in absolute value.

Original entry on oeis.org

20, 108, 414, 1936, 9872, 47732, 229714, 1134036, 5624396, 27808428, 138043018, 688575460, 3440536326, 17214566036, 86312920760, 433540643300, 2180469363652, 10980201879136, 55360485999044, 279418616308916, 1411643137279198
Offset: 1

Views

Author

R. H. Hardin Dec 26 2011

Keywords

Comments

Column 3 of A202962

Examples

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

Links

A202958 Number of arrays of n+2 integers in -4..4 with sum zero and adjacent elements differing in absolute value.

Original entry on oeis.org

36, 268, 1562, 9884, 66208, 447528, 3020170, 20430512, 139027620, 950710524, 6520317018, 44823140280, 308853569150, 2132736199028, 14754220477302, 102231808797944, 709381651755672, 4928801328948764, 34285920139143690
Offset: 1

Views

Author

R. H. Hardin Dec 26 2011

Keywords

Comments

Column 4 of A202962

Examples

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

Links

A202959 Number of arrays of n+2 integers in -5..5 with sum zero and adjacent elements differing in absolute value.

Original entry on oeis.org

62, 544, 4048, 33736, 289536, 2475008, 21274708, 184258272, 1602929218, 13990833912, 122510857450, 1075782280468, 9468706858932, 83511798894532, 737905024410346, 6530699064229052, 57882816085025096, 513698095091077304
Offset: 1

Views

Author

R. H. Hardin Dec 26 2011

Keywords

Comments

Column 5 of A202962

Examples

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

Links

A202960 Number of arrays of n+2 integers in -6..6 with sum zero and adjacent elements differing in absolute value.

Original entry on oeis.org

90, 972, 9010, 90604, 941086, 9824176, 102972822, 1085236504, 11493823804, 122199247152, 1303262970318, 13937228021316, 149401572804700, 1604863727556740, 17270995998356176, 186167832760838568
Offset: 1

Views

Author

R. H. Hardin Dec 26 2011

Keywords

Comments

Column 6 of A202962

Examples

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

Links

A202961 Number of arrays of n+2 integers in -7..7 with sum zero and adjacent elements differing in absolute value.

Original entry on oeis.org

128, 1576, 17296, 207184, 2537024, 31155004, 384996502, 4786979780, 59791891464, 749603860520, 9427927830076, 118904758131236, 1503198371854568, 19043136745799960, 241690849746856584, 3072505406058890180
Offset: 1

Views

Author

R. H. Hardin Dec 26 2011

Keywords

Comments

Column 7 of A202962

Examples

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

Links

A202963 Number of arrays of 3 integers in -n..n with sum zero and adjacent elements differing in absolute value.

Original entry on oeis.org

2, 6, 20, 36, 62, 90, 128, 168, 218, 270, 332, 396, 470, 546, 632, 720, 818, 918, 1028, 1140, 1262, 1386, 1520, 1656, 1802, 1950, 2108, 2268, 2438, 2610, 2792, 2976, 3170, 3366, 3572, 3780, 3998, 4218, 4448, 4680, 4922, 5166, 5420, 5676, 5942, 6210, 6488
Offset: 1

Views

Author

R. H. Hardin, Dec 26 2011

Keywords

Examples

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

Links

Crossrefs

Row 1 of A202962.

Formula

Empirical: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4).
Empirical g.f.: x*(2+2*x+8*x^2)/(1-2*x+2*x^3-x^4). - Colin Barker, Jan 04 2012

A202964 Number of arrays of 4 integers in -n..n with sum zero and adjacent elements differing in absolute value.

Original entry on oeis.org

4, 28, 108, 268, 544, 972, 1576, 2392, 3456, 4792, 6436, 8424, 10780, 13540, 16740, 20404, 24568, 29268, 34528, 40384, 46872, 54016, 61852, 70416, 79732, 89836, 100764, 112540, 125200, 138780, 153304, 168808, 185328, 202888, 221524, 241272
Offset: 1

Views

Author

R. H. Hardin, Dec 26 2011

Keywords

Comments

Row 2 of A202962.

Examples

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

Links

Crossrefs

Cf. A202962.

Formula

Empirical: a(n) = 3*a(n-1) -3*a(n-2) +2*a(n-3) -3*a(n-4) +3*a(n-5) -a(n-6).
Empirical g.f.: 4*x*(1 + 4*x + 9*x^2 + 5*x^3 + 5*x^4) / ((1 - x)^4*(1 + x + x^2)). - Colin Barker, Jun 03 2018

A202965 Number of arrays of 5 integers in -n..n with sum zero and adjacent elements differing in absolute value.

Original entry on oeis.org

2, 82, 414, 1562, 4048, 9010, 17296, 30648, 50232, 78388, 116614, 167824, 233858, 318234, 423094, 552554, 709104, 897434, 1120360, 1383176, 1689016, 2043772, 2450910, 2916896, 3445538, 4043906, 4716110, 5469818, 6309488, 7243362, 8276224
Offset: 1

Views

Author

R. H. Hardin, Dec 26 2011

Keywords

Comments

Row 3 of A202962.

Examples

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

Links

Crossrefs

Cf. A202962.

Formula

Empirical: a(n) = 2*a(n-1) -a(n-3) -2*a(n-5) +2*a(n-6) +a(n-8) -2*a(n-10) +a(n-11).
Empirical g.f.: 2*x*(1 + 39*x + 125*x^2 + 368*x^3 + 503*x^4 + 666*x^5 + 499*x^6 + 384*x^7 + 120*x^8 + 55*x^9) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Jun 03 2018

A202966 Number of arrays of 6 integers in -n..n with sum zero and adjacent elements differing in absolute value.

Original entry on oeis.org

0, 200, 1936, 9884, 33736, 90604, 207184, 421620, 785504, 1366876, 2251016, 3543320, 5371856, 7888384, 11270788, 15726488, 21492408, 28838244, 38069472, 49527504, 63592532, 80687412, 101276728, 125870512, 155027684, 189355324
Offset: 1

Views

Author

R. H. Hardin Dec 26 2011

Keywords

Comments

Row 4 of A202962

Examples

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

Links

Formula

Empirical: a(n) = 2*a(n-1) -3*a(n-4) +a(n-5) +a(n-6) +a(n-9) +a(n-10) -3*a(n-11) +2*a(n-14) -a(n-15)
Showing 1-10 of 13 results. Next

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