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 1-9 of 9 results.

A202658 Number of -2..2 arrays of n elements with first through fourth differences also in -2..2.

Original entry on oeis.org

5, 19, 57, 127, 213, 363, 613, 1055, 1815, 3159, 5503, 9609, 16773, 29281, 51125, 89277, 155899, 272315, 475793, 831415, 1452927, 2539213, 4437877, 7756367, 13556573, 23694815, 41415935, 72391801, 126536987, 221182305, 386622379
Offset: 1

Views

Author

R. H. Hardin Dec 22 2011

Keywords

Comments

Column 2 of A202664

Examples

			Some solutions for n=10
.-2...-2....1...-2....0....0...-1....0....0....1...-2....1....0....1...-2....2
..0...-1....2....0...-1....1....1....2....0...-1....0....0...-2....2....0....2
..0....0....2....0....0....0....1....2...-1...-2....1...-1...-2....2....0....1
..0....1....2...-1....1...-1....0....1...-1...-2....2...-1...-2....2...-1....0
..0....1....2...-1....2...-2...-1....0....0...-2....2...-1...-2....2...-2....0
..0....1....2....0....2...-2...-1....0....1...-2....2...-1...-1....1...-2....1
..1....1....1....1....2...-1...-1....0....2...-2....1...-1....1....0...-1....2
..2....0...-1....1....2....0...-1....0....2...-1....0....0....2....0....0....2
..2...-1...-2....1....1....0....0....0....1....0...-1....1....2....0....1....1
..1...-2...-2....0...-1....0....1....1....0....1...-1....0....2...-1....1....0
		

Formula

Empirical: a(n) = a(n-1) +2*a(n-3) +2*a(n-4) -a(n-5) -2*a(n-7) -a(n-8) -4*a(n-10) -7*a(n-11) -10*a(n-12) -7*a(n-13) -6*a(n-14) -a(n-15) +6*a(n-16) +9*a(n-17) +8*a(n-18) +6*a(n-19) +4*a(n-20) +2*a(n-21) for n>27

A202659 Number of -3..3 arrays of n elements with first through fourth differences also in -3..3.

Original entry on oeis.org

7, 37, 153, 475, 1101, 2591, 6055, 14199, 33289, 78119, 183447, 430889, 1011945, 2376423, 5580971, 13107163, 30782605, 72293525, 169783471, 398743229, 936465399, 2199327501, 5165208441, 12130703729, 28489466517, 66908707817
Offset: 1

Views

Author

R. H. Hardin Dec 22 2011

Keywords

Comments

Column 3 of A202664

Examples

			Some solutions for n=10
..2...-2....1....1....2...-3...-2....0....1...-3...-2....0...-1....2...-2...-3
.-1...-2....3....0....2...-1....0...-1...-1...-3...-1....1....1...-1....1...-1
.-3...-1....2....1....3....1....0....0...-1...-2...-1....1....2...-2....1....0
.-3....0....0....1....3....1...-1....1...-1...-2...-1....2....2...-1....0....0
.-1....0...-1....0....1....0...-3....2...-2...-2....0....3....2....1....0....0
..1...-1...-1....0...-1...-1...-3....2...-3...-1....0....2....2....2....0....0
..3...-1...-2....0...-2...-1...-1....1...-3....0...-1....0....2....3...-1....0
..3....0...-3...-1...-3....0....1...-1...-1....0...-1...-2....1....2...-2...-1
..1....2...-3...-2...-2....2....2...-1....1....0....0...-2....1....0...-3...-3
.-2....2...-3...-2....0....2....2....2....1....0....3....0....2....0...-3...-3
		

Formula

Empirical: a(n) = 5*a(n-1) -10*a(n-2) +15*a(n-3) -23*a(n-4) +35*a(n-5) -55*a(n-6) +70*a(n-7) -79*a(n-8) +92*a(n-9) -121*a(n-10) +134*a(n-11) -75*a(n-12) +57*a(n-13) -59*a(n-14) +38*a(n-15) +79*a(n-16) -242*a(n-17) +321*a(n-18) -392*a(n-19) +418*a(n-20) -695*a(n-21) +682*a(n-22) -386*a(n-23) +129*a(n-24) +79*a(n-25) -185*a(n-26) +488*a(n-27) -496*a(n-28) +728*a(n-29) -84*a(n-30) -854*a(n-31) +552*a(n-32) -973*a(n-33) +1092*a(n-34) -551*a(n-35) +798*a(n-36) -267*a(n-37) -405*a(n-38) +245*a(n-39) -403*a(n-40) +342*a(n-41) -135*a(n-42) +183*a(n-43) -36*a(n-44) -108*a(n-45) -23*a(n-46) +44*a(n-47) +45*a(n-48) +95*a(n-49) +34*a(n-50) -7*a(n-51) -66*a(n-52) -24*a(n-53) -52*a(n-54) +27*a(n-55) -7*a(n-56) -13*a(n-57) -14*a(n-58) -2*a(n-59) +13*a(n-60) +3*a(n-61) +a(n-62) +3*a(n-63) +a(n-64) -3*a(n-66) -a(n-68) -a(n-69) for n>78

A202660 Number of -4..4 arrays of n elements with first through fourth differences also in -4..4.

Original entry on oeis.org

9, 61, 323, 1279, 3785, 11413, 34171, 102705, 308785, 928115, 2790241, 8389429, 25223913, 75838823, 228021213, 685581997, 2061310319, 6197655253, 18634234069, 56026786211, 168453450193, 506482113541, 1522819068075, 4578597906197
Offset: 1

Views

Author

R. H. Hardin Dec 22 2011

Keywords

Comments

Column 4 of A202664

Examples

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

A202661 Number of -5..5 arrays of n elements with first through fourth differences also in -5..5.

Original entry on oeis.org

11, 91, 587, 2833, 10205, 37505, 136999, 501903, 1838983, 6737379, 24684959, 90444993, 331378703, 1214138477, 4448501629, 16298925281, 59717838711, 218801046307, 801668385089, 2937244370963, 10761811926301, 39430358807041
Offset: 1

Views

Author

R. H. Hardin Dec 22 2011

Keywords

Comments

Column 5 of A202664

Examples

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

A202662 Number of -6..6 arrays of n elements with first through fourth differences also in -6..6.

Original entry on oeis.org

13, 127, 967, 5509, 23425, 101567, 438177, 1895197, 8198571, 35463355, 153408903, 663650521, 2870932567, 12419542739, 53726653631, 232420358051, 1005444905517, 4349531110857, 18815972516807, 81397465699935, 352123564686167
Offset: 1

Views

Author

R. H. Hardin Dec 22 2011

Keywords

Comments

Column 6 of A202664

Examples

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

A202663 Number of -7..7 arrays of n elements with first through fourth differences also in -7..7.

Original entry on oeis.org

15, 169, 1483, 9739, 47713, 238453, 1186107, 5914721, 29498237, 147102833, 733637717, 3658966867, 18248551605, 91011704581, 453908063159, 2263802495143, 11290385910711, 56309167233261, 280833879734153, 1400618531203889
Offset: 1

Views

Author

R. H. Hardin, Dec 22 2011

Keywords

Comments

Column 7 of A202664.

Examples

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

Crossrefs

Cf. A202664.

A202665 Number of -n..n arrays of 5 elements with first through fourth differences also in -n..n.

Original entry on oeis.org

19, 213, 1101, 3785, 10205, 23425, 47713, 89007, 154971, 255311, 401933, 609517, 895003, 1278825, 1784361, 2438483, 3271643, 4318837, 5618137, 7213161, 9151545, 11485961, 14273951, 17579509, 21470299, 26021835, 31314591, 37435583, 44478011
Offset: 1

Views

Author

R. H. Hardin, Dec 22 2011

Keywords

Comments

Row 5 of A202664.

Examples

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

Crossrefs

Cf. A202664.

Formula

Empirical: a(n) = 2*a(n-3) +2*a(n-4) +a(n-5) -4*a(n-7) -3*a(n-8) -4*a(n-9) +2*a(n-11) +5*a(n-12) +5*a(n-13) +2*a(n-14) -4*a(n-16) -3*a(n-17) -4*a(n-18) +a(n-20) +2*a(n-21) +2*a(n-22) -a(n-25).

A202666 Number of -n..n arrays of 6 elements with first through fourth differences also in -n..n.

Original entry on oeis.org

23, 363, 2591, 11413, 37505, 101567, 238453, 503849, 979919, 1783797, 3075089, 5067465, 8035301, 12330321, 18389067, 26749755, 38062317, 53112803, 72823295, 98289495, 130780551, 171770127, 222946517, 286251779, 363870209, 458294877
Offset: 1

Views

Author

R. H. Hardin Dec 22 2011

Keywords

Comments

Row 6 of A202664

Examples

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

A202667 Number of -n..n arrays of 7 elements with first through fourth differences also in -n..n.

Original entry on oeis.org

23, 613, 6055, 34171, 136999, 438177, 1186107, 2839237, 6169921, 12410957, 23428771, 41960815, 71850731, 118414399, 188766767, 292290383, 441086445, 650648037, 940297237, 1334163773, 1861743181, 2558935713, 3468879881
Offset: 1

Views

Author

R. H. Hardin Dec 22 2011

Keywords

Comments

Row 7 of A202664

Examples

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