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 11 results. Next

A228739 Number of arrays of the median of three adjacent elements of some length n+2 0..7 array.

Original entry on oeis.org

8, 64, 512, 3312, 17088, 84288, 410828, 2037214, 10282648, 52493640, 269103944, 1379300658, 7060313768, 36093818956, 184394586102, 941828553348, 4810728325582, 24575097951832, 125549549795310, 641435496947444
Offset: 1

Views

Author

R. H. Hardin Sep 01 2013

Keywords

Comments

Column 7 of A228740

Examples

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

Links

A228744 Number of arrays of the median of three adjacent elements of some length 9 0..n array.

Original entry on oeis.org

88, 1071, 6130, 23627, 71278, 181885, 410828, 845517, 1617004, 2913955, 4999182, 8228935, 13075154, 20150881, 30239032, 44324729, 63631392, 89660791, 124237258, 169556259, 228237526, 303382949, 398639428, 518266885, 667211636, 851185323
Offset: 1

Views

Author

R. H. Hardin, Sep 01 2013

Keywords

Comments

Row 7 of A228740.

Examples

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

Links

Crossrefs

Cf. A228740.

Formula

Empirical: a(n) = (5/126)*n^7 + (4/3)*n^6 + (829/90)*n^5 + (93/4)*n^4 + (509/18)*n^3 + (221/12)*n^2 + (453/70)*n + 1.
Conjectures from Colin Barker, Mar 16 2018: (Start)
G.f.: x*(88 + 367*x + 26*x^2 - 353*x^3 + 86*x^4 - 21*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)

A228733 Number of arrays of the median of three adjacent elements of some length n+2 0..1 array.

Original entry on oeis.org

2, 4, 8, 16, 28, 50, 88, 156, 278, 496, 886, 1582, 2824, 5040, 8994, 16050, 28642, 51114, 91218, 162788, 290512, 518448, 925222, 1651150, 2946640, 5258570, 9384438, 16747458, 29887496, 53337194, 95185500, 169867942, 303146148, 540994292
Offset: 1

Views

Author

R. H. Hardin, Sep 01 2013

Keywords

Comments

Column 1 of A228740

Examples

			All solutions for n=4
..1..1..0..0..1..1..1..0..0..1..0..0..1..1..0..0
..0..1..0..0..0..1..0..1..1..1..0..1..1..0..1..0
..1..1..1..1..0..1..0..1..0..0..0..0..0..1..1..0
..1..1..1..0..1..0..0..0..0..0..1..1..1..0..1..0

Links

Formula

Empirical: a(n) = 2*a(n-1) -a(n-3) +a(n-5).
Empirical: G.f. -2*x*(1+x)*(x^2-x+1) / ( -1+2*x-x^3+x^5 ). - R. J. Mathar, Sep 02 2013

A228734 Number of arrays of the median of three adjacent elements of some length n+2 0..2 array.

Original entry on oeis.org

3, 9, 27, 77, 185, 447, 1071, 2593, 6333, 15513, 38039, 93213, 228279, 558849, 1367945, 3348489, 8196847, 20065943, 49122291, 120253773, 294386457, 720668887, 1764221329, 4318870217, 10572732933, 25882394413, 63360952825, 155109705901
Offset: 1

Views

Author

R. H. Hardin Sep 01 2013

Keywords

Examples

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

Links

Crossrefs

Column 2 of A228740.

Formula

Empirical: a(n) = 3*a(n-1) -a(n-2) -2*a(n-3) +a(n-4) +5*a(n-5) -2*a(n-6) +a(n-7) +a(n-9) +a(n-10) -2*a(n-12) -a(n-13) +a(n-14)

A228735 Number of arrays of the median of three adjacent elements of some length -(n+2) 0..3 array.

Original entry on oeis.org

4, 16, 64, 232, 696, 2072, 6130, 18378, 55716, 169734, 517764, 1578184, 4806344, 14629384, 44519552, 135480532, 412314438, 1254882280, 3819338704, 11624541548, 35380360780, 107682931160, 327740673246, 997501106370, 3035962621026
Offset: 1

Views

Author

R. H. Hardin Sep 01 2013

Keywords

Examples

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

Links

Crossrefs

Column 3 of A228740.

Formula

Empirical: a(n) = 4*a(n-1) -2*a(n-2) -6*a(n-3) +6*a(n-4) +15*a(n-5) -11*a(n-6) +a(n-7) +a(n-8) +3*a(n-9) +24*a(n-10) -3*a(n-11) -35*a(n-12) -28*a(n-13) +22*a(n-14) +18*a(n-15) -9*a(n-16) -11*a(n-17) -4*a(n-18) +15*a(n-19) +15*a(n-20) -2*a(n-21) -4*a(n-22) -4*a(n-23) -3*a(n-24) +a(n-25) +a(n-26)

A228736 Number of arrays of the median of three adjacent elements of some length-(n+2) 0..4 array.

Original entry on oeis.org

5, 25, 125, 545, 1943, 6797, 23627, 83391, 298239, 1073743, 3873051, 13959617, 50261845, 180829983, 650385801, 2339156205, 8413500735, 30263904639, 108865370619, 391615337877, 1408733302733, 5067520822187, 18228904185829
Offset: 1

Views

Author

R. H. Hardin Sep 01 2013

Keywords

Examples

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

Links

Crossrefs

Column 4 of A228740.

Formula

Empirical: a(n) = 5*a(n-1) -4*a(n-2) -10*a(n-3) +16*a(n-4) +34*a(n-5) -46*a(n-6) +18*a(n-7) +15*a(n-8) +8*a(n-9) +129*a(n-10) +8*a(n-11) -283*a(n-12) -285*a(n-13) +291*a(n-14) +129*a(n-15) -281*a(n-16) -492*a(n-17) +132*a(n-18) +913*a(n-19) +760*a(n-20) +57*a(n-21) -727*a(n-22) -370*a(n-23) +74*a(n-24) +38*a(n-25) -59*a(n-26) -628*a(n-27) -241*a(n-28) +448*a(n-29) +443*a(n-30) +391*a(n-31) -32*a(n-32) -342*a(n-33) -158*a(n-34) -36*a(n-35) +40*a(n-36) +75*a(n-37) +13*a(n-38) -8*a(n-39) -4*a(n-40) -5*a(n-41) +a(n-43)

A228737 Number of arrays of the median of three adjacent elements of some length n+2 0..5 array.

Original entry on oeis.org

6, 36, 216, 1096, 4504, 17986, 71278, 287154, 1174282, 4842316, 20019620, 82713844, 341336666, 1407252850, 5799332126, 23897370232, 98480668292, 405872225912, 1672825694744, 6894787036372, 28417852764586, 117127559374180
Offset: 1

Views

Author

R. H. Hardin Sep 01 2013

Keywords

Comments

Column 5 of A228740

Examples

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

Links

A228738 Number of arrays of the median of three adjacent elements of some length n+2 0..6 array.

Original entry on oeis.org

7, 49, 343, 1981, 9191, 41083, 181885, 819099, 3749921, 17338503, 80437853, 373008019, 1727505765, 7991536851, 36949011409, 170810543525, 789678726959, 3651141596711, 16882484843753, 78065155382933, 360977446471839
Offset: 1

Views

Author

R. H. Hardin, Sep 01 2013

Keywords

Comments

Column 6 of A228740.

Examples

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

Links

A228741 Number of arrays of the median of three adjacent elements of some length-6 0..n array.

Original entry on oeis.org

16, 77, 232, 545, 1096, 1981, 3312, 5217, 7840, 11341, 15896, 21697, 28952, 37885, 48736, 61761, 77232, 95437, 116680, 141281, 169576, 201917, 238672, 280225, 326976, 379341, 437752, 502657, 574520, 653821, 741056, 836737, 941392, 1055565
Offset: 1

Views

Author

R. H. Hardin, Sep 01 2013

Keywords

Examples

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

Links

Crossrefs

Row 4 of A228740.

Formula

Empirical: a(n) = (n+1)*(2*n^3+10*n^2+9*n+3)/3.
Empirical: G.f. -x*(16-3*x+7*x^2-5*x^3+x^4) / (x-1)^5 . - R. J. Mathar, Sep 02 2013

A228742 Number of arrays of the median of three adjacent elements of some length 7 0..n array.

Original entry on oeis.org

28, 185, 696, 1943, 4504, 9191, 17088, 29589, 48436, 75757, 114104, 166491, 236432, 327979, 445760, 595017, 781644, 1012225, 1294072, 1635263, 2044680, 2532047, 3107968, 3783965, 4572516, 5487093, 6542200, 7753411, 9137408, 10712019
Offset: 1

Views

Author

R. H. Hardin, Sep 01 2013

Keywords

Comments

Row 5 of A228740

Examples

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

Links

Formula

Empirical: a(n) = (n+1)*(19*n^4+186*n^3+349*n^2+226*n+60)/60.
Empirical: G.f. -x*(-28-17*x-6*x^2+18*x^3-6*x^4+x^5) / (x-1)^6. - R. J. Mathar, Sep 02 2013
Showing 1-10 of 11 results. Next

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