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 41-48 of 48 results.

A125541 Number of n X n arrays with entries in 1..9 in which adjacent entries differ by 6 or less (adjacent means in x or y directions).

Original entry on oeis.org

1, 9, 4999, 183051647, 432993880473035, 66327998573151304476953, 657786158098403835519781868703261, 422337116619421509499034109697459735541947069
Offset: 0

Views

Author

R. H. Hardin, Dec 31 2006

Keywords

Comments

[Empirical] a(base+1,n,diff)=a(base,n,diff)+F(n,diff) for base>=2.diff.(n-1) and F(n,diff)= (n=2, A063496(diff+1)) (n=3, A068744(diff+1)) (n=4, A068745(diff+1)) (n=5, A068746(diff+1)) (n=6, A068747(diff+1))

A125542 Number of n X n arrays with entries in 1..9 in which adjacent entries differ by 7 or less (adjacent means in x or y directions).

Original entry on oeis.org

1, 9, 5987, 299369303, 1119629504911493, 313365607149624564094821, 6563186624029432821357130152132207, 10286477666057808275996577778629802367615683611
Offset: 0

Views

Author

R. H. Hardin, Dec 31 2006

Keywords

Comments

[Empirical] a(base+1,n,diff)=a(base,n,diff)+F(n,diff) for base>=2.diff.(n-1) and F(n,diff)= (n=2, A063496(diff+1)) (n=3, A068744(diff+1)) (n=4, A068745(diff+1)) (n=5, A068746(diff+1)) (n=6, A068747(diff+1))

A125543 Number of n X n arrays with entries in 1..10 in which adjacent entries differ by 7 or less (adjacent means in x or y directions).

Original entry on oeis.org

1, 10, 8022, 543128374, 3055705944761702, 1431275227278696138328486, 55801019314977359729825524189282042, 181083160867536477536139285619272596798948123330
Offset: 0

Views

Author

R. H. Hardin, Dec 31 2006

Keywords

Comments

[Empirical] a(base+1,n,diff)=a(base,n,diff)+F(n,diff) for base>=2.diff.(n-1) and F(n,diff)= (n=2, A063496(diff+1)) (n=3, A068744(diff+1)) (n=4, A068745(diff+1)) (n=5, A068746(diff+1)) (n=6, A068747(diff+1))

A125544 Number of n X n arrays with entries in 1..10 in which adjacent entries differ by 8 or less (adjacent means in x or y directions).

Original entry on oeis.org

1, 10, 9282, 809972882, 6620278776930050, 5070242688355834000238994, 363841631496359667433584638167920450, 2446405761143101128307819275435459905126486602002
Offset: 0

Views

Author

R. H. Hardin, Dec 31 2006

Keywords

Comments

[Empirical] a(base+1,n,diff) = a(base,n,diff) + F(n,diff) for base>=2.diff.(n-1) and F(n,diff) = (n=2, A063496(diff+1)) (n=3, A068744(diff+1)) (n=4, A068745(diff+1)) (n=5, A068746(diff+1)) (n=6, A068747(diff+1)).

A125545 Number of n X n arrays with entries in 1..11 in which adjacent entries differ by 8 or less (adjacent means in x or y directions).

Original entry on oeis.org

1, 11, 12199, 1419562557, 17124710891367659, 21446024690051517579350807, 2787767647614213119983106320870299629, 37614839219636718408474282959362229237375107365087
Offset: 0

Views

Author

R. H. Hardin, Dec 31 2006

Keywords

Comments

[Empirical] a(base+1,n,diff)=a(base,n,diff)+F(n,diff) for base>=2.diff.(n-1) and F(n,diff)= (n=2, A063496(diff+1)) (n=3, A068744(diff+1)) (n=4, A068745(diff+1)) (n=5, A068746(diff+1)) (n=6, A068747(diff+1))

A125546 Number of n X n arrays with entries in 1..11 in which adjacent entries differ by 9 or less (adjacent means in x or y directions).

Original entry on oeis.org

1, 11, 13763, 1978210109, 32571675386972165, 61452459671072911580420687, 13284933102293631737361621573688797935, 329079799821925392118398338649907446164698978078433
Offset: 0

Views

Author

R. H. Hardin, Dec 31 2006

Keywords

Comments

[Empirical] a(base+1,n,diff)=a(base,n,diff)+F(n,diff) for base>=2.diff.(n-1) and F(n,diff)= (n=2, A063496(diff+1)) (n=3, A068744(diff+1)) (n=4, A068745(diff+1)) (n=5, A068746(diff+1)) (n=6, A068747(diff+1))

A125547 Number of n X n arrays with entries in 1..12 in which adjacent entries differ by 9 or less (adjacent means in x or y directions).

Original entry on oeis.org

1, 12, 17782, 3359860178, 80173083905265254, 241867388512389264991124102, 92239510661284205765199147022065188442, 4446848187806762069273466271591426934850445380022534
Offset: 0

Views

Author

R. H. Hardin, Dec 31 2006

Keywords

Comments

[Empirical] a(base+1,n,diff) = a(base,n,diff)+F(n,diff) for base>=2.diff.(n-1) and F(n,diff) = (n = 2, A063496(diff+1)) (n = 3, A068744(diff+1)) (n = 4, A068745(diff+1)) (n = 5, A068746(diff+1)) (n = 6, A068747(diff+1))

A175197 Array A(k,n) of the number of points of the A_k lattice with maximum infinity norm n, read by antidiagonals.

Original entry on oeis.org

1, 1, 0, 1, 2, 0, 1, 6, 2, 0, 1, 18, 12, 2, 0, 1, 50, 66, 18, 2, 0, 1, 140, 330, 146, 24, 2, 0, 1, 392, 1610, 1070, 258, 30, 2, 0, 1, 1106, 7742, 7580, 2500, 402, 36, 2, 0, 1, 3138, 37058, 52556, 23330, 4850, 578, 42, 2, 0, 1, 8952, 177186, 360402, 212436, 56252, 8350, 786
Offset: 0

Views

Author

R. J. Mathar, Mar 02 2010

Keywords

Comments

The values are computed starting with an auxiliary array which places the centered trinomial numbers A002426, the centered pentanomial numbers A005191, the centered 7-nomial numbers A025012 etc. into separate columns:
.1,....1,......1,.......1,........1,........1,.........1,.........1,.........1
.1,....3,......5,.......7,........9,.......11,........13,........15,........17
.1,....7,.....19,......37,.......61,.......91,.......127,.......169,.......217
.1,...19,.....85,.....231,......489,......891,......1469,......2255,......3281
.1,...51,....381,....1451,.....3951,.....8801,.....17151,.....30381,.....50101
.1,..141,...1751,....9331,....32661,....88913,....204763,....418503,....782153
.1,..393,...8135,...60691,...273127,...908755,...2473325,...5832765,..12354469
.1,.1107,..38165,..398567,..2306025,..9377467,..30162301,..82073295,.197018321
.1,.3139,.180325,.2636263,.19610233,.97464799,.370487485,1163205475,3164588407
This is a subarray of A077042. Rows are A005408, A003215, A063496, A083669 (see A077044) etc. The array A(k,n) is the first differences along each row of this auxiliary array.

Examples

			A(k,n) starts in row k=0, column n=0 as:
1,....0,......0,.......0,........0,........0,.........0,.........0,.........0
1,....2,......2,.......2,........2,........2,.........2,.........2,.........2
1,....6,.....12,......18,.......24,.......30,........36,........42,........48
1,...18,.....66,.....146,......258,......402,.......578,.......786,......1026
1,...50,....330,....1070,.....2500,.....4850,......8350,.....13230,.....19720
1,..140,...1610,....7580,....23330,....56252,....115850,....213740,....363650
1,..392,...7742,...52556,...212436,...635628,...1564570,...3359440,...6521704
1,.1106,..37058,..360402,..1907458,..7071442,..20784834,..51910994,.114945026
1,.3138,.177186,.2455938,.16973970,.77854566,.273022686,.792717990,2001382932

Links

Crossrefs

Cf. A008458 (row k=2), A010006 (row k=3), A110907.
Previous Showing 41-48 of 48 results.

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