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 14 results. Next

A231757 Number of (n+1)X(n+1) 0..1 arrays with no element having a strict majority of its horizontal, diagonal and antidiagonal neighbors equal to one.

Original entry on oeis.org

9, 136, 5041, 493695, 175642009, 216545491864, 682267982467600, 6184663140527966655, 184835030323441507989529, 17039092957711747812559207879, 4549223325244087259619117440725081
Offset: 1

Views

Author

R. H. Hardin, Nov 13 2013

Keywords

Comments

Diagonal of A231764

Examples

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

A231758 Number of (n+1)X(2+1) 0..1 arrays with no element having a strict majority of its horizontal, diagonal and antidiagonal neighbors equal to one.

Original entry on oeis.org

33, 136, 660, 3213, 14989, 70927, 338352, 1603633, 7596720, 36066272, 171140301, 811651995, 3850637109, 18269376384, 86668158745, 411153474416, 1950577525332, 9253691650061, 43899995716425, 208265361505983, 988028267125504
Offset: 1

Views

Author

R. H. Hardin, Nov 13 2013

Keywords

Comments

Column 2 of A231764

Examples

			Some solutions for n=6
..0..0..0....1..0..0....1..0..0....0..0..0....0..0..1....1..0..0....0..0..0
..1..0..1....1..1..0....0..1..1....1..0..0....0..0..0....1..0..0....1..0..1
..0..1..1....0..0..1....0..0..0....1..0..1....1..1..1....1..1..0....1..0..0
..0..0..0....0..0..1....1..0..0....0..0..0....0..0..1....1..0..0....0..0..0
..0..0..0....1..0..0....1..0..0....1..0..0....0..0..0....1..0..0....0..1..0
..1..1..0....0..1..1....0..0..0....0..1..1....1..0..1....0..1..1....0..0..0
..0..0..1....0..0..0....1..1..0....0..0..1....0..1..0....1..0..0....1..0..0
		

Formula

Empirical: a(n) = 3*a(n-1) +47*a(n-3) -25*a(n-4) +21*a(n-5) -403*a(n-6) +110*a(n-7) +40*a(n-8) +1601*a(n-9) -348*a(n-10) -520*a(n-11) -2656*a(n-12) +792*a(n-13) +288*a(n-14) +2480*a(n-15) -544*a(n-16) +128*a(n-17) -1600*a(n-18) +128*a(n-19) +512*a(n-21)

A231759 Number of (n+1)X(3+1) 0..1 arrays with no element having a strict majority of its horizontal, diagonal and antidiagonal neighbors equal to one.

Original entry on oeis.org

100, 625, 5041, 40000, 303601, 2353156, 18318400, 141681409, 1096603225, 8501393209, 65862549769, 510117350625, 3952044600625, 30617619155761, 237184671441601, 1837438830737449, 14234617914330724, 110274092537986624
Offset: 1

Views

Author

R. H. Hardin, Nov 13 2013

Keywords

Comments

Column 3 of A231764

Examples

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

Formula

Empirical: a(n) = 4*a(n-1) +12*a(n-2) +149*a(n-3) +34*a(n-4) -745*a(n-5) -4377*a(n-6) -1298*a(n-7) +13107*a(n-8) +52121*a(n-9) +8083*a(n-10) -86996*a(n-11) -321488*a(n-12) -28134*a(n-13) +269200*a(n-14) +1028451*a(n-15) +72948*a(n-16) -507872*a(n-17) -2031587*a(n-18) -253166*a(n-19) +609639*a(n-20) +2548479*a(n-21) +414970*a(n-22) -482501*a(n-23) -2033465*a(n-24) -288069*a(n-25) +243904*a(n-26) +1017882*a(n-27) +103832*a(n-28) -88438*a(n-29) -327567*a(n-30) -19692*a(n-31) +23162*a(n-32) +69365*a(n-33) +1980*a(n-34) -4140*a(n-35) -9617*a(n-36) -152*a(n-37) +478*a(n-38) +849*a(n-39) +16*a(n-40) -33*a(n-41) -44*a(n-42) -a(n-43) +a(n-44) +a(n-45)

A231760 Number of (n+1)X(4+1) 0..1 arrays with no element having a strict majority of its horizontal, diagonal and antidiagonal neighbors equal to one.

Original entry on oeis.org

315, 2976, 38160, 493695, 5879679, 71884125, 893571840, 10965349591, 134407778400, 1654812479232, 20352945004533, 250055045333667, 3074220674469117, 37799970801628952, 464662025973498675
Offset: 1

Views

Author

R. H. Hardin, Nov 13 2013

Keywords

Comments

Column 4 of A231764

Examples

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

A231761 Number of (n+1)X(5+1) 0..1 arrays with no element having a strict majority of its horizontal, diagonal and antidiagonal neighbors equal to one.

Original entry on oeis.org

961, 15625, 356409, 8231161, 175642009, 3855664836, 85629975876, 1881009507001, 41320353904281, 910635938795025, 20049876927417744, 441133454459003524, 9710711221453585281, 213776317733333022369, 4705328739274857392400
Offset: 1

Views

Author

R. H. Hardin, Nov 13 2013

Keywords

Comments

Column 5 of A231764

Examples

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

A231762 Number of (n+1)X(6+1) 0..1 arrays with no element having a strict majority of its horizontal, diagonal and antidiagonal neighbors equal to one.

Original entry on oeis.org

3024, 84817, 3453471, 143424652, 5493044921, 216545491864, 8624298007460, 340129511751843, 13416072442152345, 530629269304561623, 20970654950669865441, 828283329242364336935, 32728464710431240780113
Offset: 1

Views

Author

R. H. Hardin, Nov 13 2013

Keywords

Comments

Column 6 of A231764

Examples

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

A231763 Number of (n+1)X(7+1) 0..1 arrays with no element having a strict majority of its horizontal, diagonal and antidiagonal neighbors equal to one.

Original entry on oeis.org

9409, 440896, 30958096, 2217939025, 146247350929, 9934984224361, 682267982467600, 46367367209812224, 3151689997684400676, 214862774587748825616, 14634892191955776597081, 996191537899297169858481
Offset: 1

Views

Author

R. H. Hardin, Nov 13 2013

Keywords

Comments

Column 7 of A231764

Examples

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

A231765 Number of (1+1) X (n+1) 0..1 arrays with no element having a strict majority of its horizontal, diagonal and antidiagonal neighbors equal to one.

Original entry on oeis.org

9, 33, 100, 315, 961, 3024, 9409, 29319, 91204, 284279, 885481, 2758192, 8590761, 26760591, 83356900, 259648623, 808776721, 2519272112, 7847302225, 24443615655, 76139572356, 237167776135, 738755721081, 2301155717168, 7167887098681
Offset: 1

Views

Author

R. H. Hardin, Nov 13 2013

Keywords

Examples

			Some solutions for n=7:
..0..0..0..0..0..1..0..0....1..0..0..0..0..1..0..0....0..1..1..0..0..1..0..0
..0..1..0..0..1..0..1..0....1..1..0..0..0..0..0..0....0..0..0..1..0..0..1..0
		

Crossrefs

Row 1 of A231764.

Formula

Empirical: a(n) = 3*a(n-1) + a(n-3) + 7*a(n-4) - 20*a(n-5) - 2*a(n-6) - 4*a(n-8) + 8*a(n-9).
Empirical g.f.: x*(9 + 6*x + x^2 + 6*x^3 - 80*x^4 - 10*x^5 - 8*x^7 + 32*x^8) / ((1 - 3*x - x^2 + 2*x^3)*(1 + x^2 - 6*x^4 - 4*x^6)). - Colin Barker, Oct 01 2018

A231766 Number of (2+1)X(n+1) 0..1 arrays with no element having a strict majority of its horizontal, diagonal and antidiagonal neighbors equal to one.

Original entry on oeis.org

16, 136, 625, 2976, 15625, 84817, 440896, 2280000, 11902500, 62359187, 325513764, 1697812287, 8864034201, 46293362688, 241690224400, 1261713925692, 6587266165489, 34392457554368, 179559008401369, 937448116348715
Offset: 1

Views

Author

R. H. Hardin, Nov 13 2013

Keywords

Comments

Row 2 of A231764

Examples

			Some solutions for n=6
..0..0..0..0..1..1..0....0..0..0..1..1..0..0....0..1..1..0..0..0..1
..0..0..0..1..0..0..0....0..0..0..1..0..0..1....1..0..0..1..0..0..0
..1..1..0..0..1..0..1....1..1..0..0..1..0..0....0..0..0..0..0..0..1
		

Formula

Empirical: a(n) = 4*a(n-1) +25*a(n-3) +92*a(n-4) -199*a(n-5) -51*a(n-6) -940*a(n-7) -2001*a(n-8) +1652*a(n-9) -54*a(n-10) +6797*a(n-11) +11789*a(n-12) -5313*a(n-13) +1302*a(n-14) -17859*a(n-15) -25925*a(n-16) +7454*a(n-17) -951*a(n-18) +18218*a(n-19) +22763*a(n-20) -3531*a(n-21) +270*a(n-22) -7326*a(n-23) -8414*a(n-24) +641*a(n-25) -33*a(n-26) +1169*a(n-27) +1281*a(n-28) -43*a(n-29) +3*a(n-30) -67*a(n-31) -71*a(n-32) +a(n-33) +a(n-35) +a(n-36)

A231767 Number of (3+1)X(n+1) 0..1 arrays with no element having a strict majority of its horizontal, diagonal and antidiagonal neighbors equal to one.

Original entry on oeis.org

36, 660, 5041, 38160, 356409, 3453471, 30958096, 275036364, 2497000900, 22773363171, 206128712196, 1863472732275, 16885039757881, 153067510948440, 1386533696771344, 12557954163081200, 113765768465994225
Offset: 1

Views

Author

R. H. Hardin, Nov 13 2013

Keywords

Comments

Row 3 of A231764

Examples

			Some solutions for n=4
..1..0..0..1..0....0..0..0..0..0....0..0..1..0..0....0..1..1..1..0
..0..0..1..0..1....0..0..1..1..1....1..0..0..0..1....1..0..0..0..0
..0..0..0..0..0....1..0..0..0..0....0..1..0..0..0....0..0..1..0..0
..0..0..1..0..0....0..0..0..0..0....1..0..1..1..1....0..1..1..1..0
		
Showing 1-10 of 14 results. Next