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 1-4 of 4 results.

A158261 a(n) = coefficient of x^n in the (2^(n-1))-th iteration of x+x^2 for n>=1.

Original entry on oeis.org

1, 2, 12, 364, 49280, 27297360, 59855127360, 515600292989376, 17478262497392546432, 2341170788069821884925696, 1243964516830446590036473921536, 2629751195406987463208250109864126464
Offset: 1

Views

Author

Paul D. Hanna, Mar 15 2009

Keywords

Examples

			Table of coefficients in the (2^i)-th iteration of x+x^2 begins:
(1),1;
1,(2),2,1;
1,4,(12),30,64,118,188,258,302,298,244,162,84,32,8,1;
1,8,56,(364),2240,13188,74760,409836,2179556,11271436,56788112,...;
1,16,240,3480,(49280),685160,9383248,126855288,1695695976,...;
1,32,992,30256,912640,(27297360),810903456,23950328688,...;
1,64,4032,252000,15665664,969917088,(59855127360),3683654668512,...;
1,128,16256,2056384,259445760,32668147008,4106848523904,(515600292989376),...;
1,256,65280,16613760,4222658560,1072200161920,272033712041216,68973668731925376,(17478262497392546432),...;
...
where the terms in parenthesis form the initial terms of this sequence.

Links

Crossrefs

Cf. A158260, A158262, A158263, A158264 (table).

Programs

  • PARI
    {a(n)=local(G=x+x^2+x*O(x^n)); if(n<0, 0, for(i=1, n-1, G=subst(G, x, G+x*O(x^n))); polcoeff(G, n, x))}

A158260 a(n) = coefficient of x^n in the [2^(n-2)]-th iteration of x+x^2 for n>=2.

Original entry on oeis.org

1, 2, 30, 2240, 685160, 810903456, 3683654668512, 64657586863790400, 4426882384548801561472, 1192052411353154132337483776, 1270174918862853255008627489608704
Offset: 2

Views

Author

Paul D. Hanna, Mar 15 2009

Keywords

Examples

			Table of coefficients in the (2^i)-th iteration of x+x^2 begins:
1,(1);
1,2,(2),1;
1,4,12,(30),64,118,188,258,302,298,244,162,84,32,8,1;
1,8,56,364,(2240),13188,74760,409836,2179556,11271436,56788112,...;
1,16,240,3480,49280,(685160),9383248,126855288,1695695976,...;
1,32,992,30256,912640,27297360,(810903456),23950328688,...;
1,64,4032,252000,15665664,969917088,59855127360,(3683654668512),...;
1,128,16256,2056384,259445760,32668147008,4106848523904,515600292989376,(64657586863790400),...;
...
where the terms in parenthesis form the initial terms of this sequence.

Crossrefs

Cf. A158261, A158262, A158263, A158264 (table).

Programs

  • PARI
    {a(n)=local(G=x+x^2+x*O(x^n)); if(n<2, 0, for(i=1, n-2, G=subst(G, x, G)); polcoeff(G, n, x))}

A158262 a(n) = coefficient of x^n in the (2^n)-th iteration of x+x^2 for n>=1.

Original entry on oeis.org

1, 4, 56, 3480, 912640, 969917088, 4106848523904, 68973668731925376, 4597014244761562326272, 1218175506582318206655794688, 1285897546575275148015361075150848
Offset: 1

Views

Author

Paul D. Hanna, Mar 15 2009

Keywords

Examples

			Table of coefficients in the (2^i)-th iteration of x+x^2 begins:
1,1;
(1),2,2,1;
1,(4),12,30,64,118,188,258,302,298,244,162,84,32,8,1;
1,8,(56),364,2240,13188,74760,409836,2179556,11271436,56788112,...;
1,16,240,(3480),49280,685160,9383248,126855288,1695695976,...;
1,32,992,30256,(912640),27297360,810903456,23950328688,...;
1,64,4032,252000,15665664,(969917088),59855127360,3683654668512,...;
1,128,16256,2056384,259445760,32668147008,(4106848523904),...;
1,256,65280,16613760,4222658560,1072200161920,272033712041216,(68973668731925376),...;
...
Where the terms in parenthesis form the initial terms of this sequence.

Crossrefs

Cf. A158260, A158261, A158263, A158264 (table).

Programs

  • PARI
    {a(n)=local(G=x+x^2+x*O(x^n)); if(n<0, 0, for(i=1, n, G=subst(G, x, G+x*O(x^n))); polcoeff(G, n, x))}

A158263 a(n) = coefficient of x^n in the (2^(n+1))-th iteration of x+x^2 for n>=1.

Original entry on oeis.org

1, 8, 240, 30256, 15665664, 32668147008, 272033712041216, 9024264001164470016, 1192791193150627685091840, 628748300357129103400036998144, 1322980853407936018020929177243811840
Offset: 1

Views

Author

Paul D. Hanna, Mar 15 2009

Keywords

Examples

			Table of coefficients in the (2^i)-th iteration of x+x^2 begins:
1,1;
1,2,2,1;
(1),4,12,30,64,118,188,258,302,298,244,162,84,32,8,1;
1,(8),56,364,2240,13188,74760,409836,2179556,11271436,56788112,...;
1,16,(240),3480,49280,685160,9383248,126855288,1695695976,...;
1,32,992,(30256),912640,27297360,810903456,23950328688,...;
1,64,4032,252000,(15665664),969917088,59855127360,3683654668512,...;
1,128,16256,2056384,259445760,(32668147008),4106848523904,...;
1,256,65280,16613760,4222658560,1072200161920,(272033712041216),...;
1,512,261632,133563136,68139438080,34745409189120,17710292513905152,(9024264001164470016),...;
...
Where the terms in parenthesis form the initial terms of this sequence.

Crossrefs

Cf. A158260, A158261, A158262, A158264 (table).

Programs

  • PARI
    {a(n)=local(G=x+x^2+x*O(x^n)); if(n<0, 0, for(i=1, n+1, G=subst(G, x, G+x*O(x^n))); polcoeff(G, n, x))}
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.