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 1-5 of 5 results.

A088889 Polynexus numbers of order 8.

Original entry on oeis.org

0, 1, 26, 245, 1353, 5368, 17017, 45878, 109446, 237291, 476476, 898403, 1607255, 2750202, 4529539, 7216924, 11169884, 16850757, 24848238, 35901697, 50928437, 71054060, 97646109, 132351154, 177135490, 234329615, 306676656, 397384911, 510184675, 649389518
Offset: 1

Views

Author

Xavier Acloque, Oct 21 2003

Keywords

Links

Crossrefs

Cf. A079547, A083200, A088890, A088891, A088892, A088893, A088894.

Programs

  • Mathematica
    Table[((n^8 - (n - 1)^8) - (n^4 - (n - 1)^4))/240, {n, 26}] (* Bruno Berselli, Feb 10 2012 *)
LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{0,1,26,245,1353,5368,17017,45878},30] (* Harvey P. Dale, Oct 31 2024 *)

Formula

a(n) = ((n^8-(n-1)^8)-(n^4-(n-1)^4))/240 = ((n^8-(n-1)^8)-(n^4-(n-1)^4))/(2^8-2^4).
G.f.: x^2*(1+x)*(1+17*x+48*x^2+17*x^3+x^4)/(1-x)^8. - Bruno Berselli, Feb 10 2012

Extensions

First term added according to the formula from Bruno Berselli, Feb 10 2012

A088894 Polynexus numbers of order 16.

Original entry on oeis.org

0, 1, 656, 64895, 2263323, 40728358, 464160877, 3788798018, 23985732786, 124343403711, 548683300726, 2120490369833, 7334132330405, 23085114905772, 67009386720139, 181293280189204, 461148470725844, 1110780513139917, 2548868780082828, 5600100525524707
Offset: 1

Views

Author

Xavier Acloque, Oct 21 2003

Keywords

Links

Crossrefs

Cf. A079547, A083200, A088889, A088890, A088891, A088892, A088893.

Programs

  • Mathematica
    Table[((n^16 - (n - 1)^16) - (n^4 - (n - 1)^4))/65520, {n, 20}] (* Bruno Berselli, Feb 08 2012 *)

Formula

a(n) = ((n^16-(n-1)^16)-(n^4-(n-1)^4))/65520 = ((n^16-(n-1)^16)-(n^4-(n-1)^4))/(2^16-2^4).
G.f.: x^2*(1+x)*(1+639*x+53880*x^2+1249283*x^3+10687767*x^4+38266494*x^5+59151072*x^6+38266494*x^7+10687767*x^8+1249283*x^9+53880*x^10+639*x^11+x^12)/(1-x)^16. - Bruno Berselli, Feb 08 2012

Extensions

First term added according to the formula from Bruno Berselli, Feb 08 2012

A088891 Polynexus numbers of order 9.

Original entry on oeis.org

0, 1, 38, 481, 3355, 16120, 60071, 186238, 502386, 1215435, 2694340, 5559191, 10803013, 19953466, 35282365, 60071660, 98945236, 158276613, 246683346, 375619645, 560079455, 819422956, 1178340163, 1667966026, 2327162150, 3203980975, 4357328976, 5858846163
Offset: 1

Views

Author

Xavier Acloque, Oct 21 2003

Keywords

Links

Crossrefs

Cf. A079547, A083200, A088889, A088890, A088892, A088893, A088894.

Programs

  • Mathematica
    Table[((n^9-(n-1)^9)-(n^3-(n-1)^3))/504,{n,30}] (* or *) LinearRecurrence[ {9,-36,84,-126,126,-84,36,-9,1},{0,1,38,481,3355,16120,60071,186238,502386},30] (* Harvey P. Dale, Jan 18 2012 *)

Formula

a(n) = ((n^9-(n-1)^9)-(n^3-(n-1)^3))/504 = ((n^9-(n-1)^9)-(n^3-(n-1)^3))/(2^9-2^3).
a(1)=1, a(2)=38, a(3)=481, a(4)=3355, a(5)=16120, a(6)=60071, a(7)=186238, a(8)=502386, a(9)=1215435, a(n)=9*a(n-1)-36*a(n-2)+ 84*a(n-3)- 126*a(n-4)+126*a(n-5)-84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9). - Harvey P. Dale, Jan 18 2012
G.f.: x^2*(1+29*x+175*x^2+310*x^3+175*x^4+29*x^5+x^6)/(1-x)^9. - Bruno Berselli, Feb 10 2012

Extensions

Offset changed and first term added (according to the formula) from Bruno Berselli, Feb 08 2012

A088892 Polynexus numbers of order 14.

Original entry on oeis.org

0, 1, 291, 16096, 356232, 4411517, 36621423, 227095448, 1128128568, 4708376529, 17078744419, 55199550120, 161993768080, 438011626365, 1103841220991, 2616890599056, 5880356075792, 12602902382337, 25897027973187, 51245013077968, 98017089897528, 181801058663389
Offset: 1

Views

Author

Xavier Acloque, Oct 21 2003

Keywords

Links

Crossrefs

Cf. A079547, A083200, A088889, A088890, A088891, A088893, A088894.

Programs

  • Mathematica
    Table[((n^14 - (n - 1)^14) - (n^2 - (n - 1)^2))/16380, {n, 20}] (* Bruno Berselli, Feb 08 2012 *)
LinearRecurrence[{14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1},{0,1,291,16096,356232,4411517,36621423,227095448,1128128568,4708376529,17078744419,55199550120,161993768080,438011626365},20] (* Harvey P. Dale, Mar 04 2024 *)

Formula

a(n) = ((n^14-(n-1)^14)-(n^2-(n-1)^2))/16380 = ((n^14-(n-1)^14)-(n^2-(n-1)^2))/(2^14-2^2).
G.f.: x^2*(1+x)*(1+276*x+11837*x^2+145168*x^3+638914*x^4+1068728*x^5+638914*x^6+145168*x^7+11837*x^8+276*x^9+x^10)/(1-x)^14. - Bruno Berselli, Feb 08 2012

Extensions

First term added according to the formula from Bruno Berselli, Feb 08 2012

A088893 Polynexus numbers of order 15.

Original entry on oeis.org

0, 1, 437, 32338, 898774, 13420861, 130567049, 929084572, 5210829060, 24240197433, 96985597357, 342789175982, 1092151142842, 3186269918917, 8618003504977, 21826239750488, 52182586901800, 118565859736497, 257462955231909, 536839834252906, 1079191653936254
Offset: 1

Views

Author

Xavier Acloque, Oct 21 2003

Keywords

Links

Crossrefs

Cf. A079547, A083200, A088889, A088890, A088891, A088892, A088894.

Programs

  • Mathematica
    Table[((n^15 - (n - 1)^15) - (n^3 - (n - 1)^3))/32760, {n, 20}] (* Bruno Berselli, Feb 08 2012 *)

Formula

a(n) = ((n^15-(n-1)^15)-(n^3-(n-1)^3))/32760 = ((n^15-(n-1)^15)-(n^3-(n-1)^3))/(2^15-2^3).
G.f.: x^2*(1+422*x+25888*x^2+459134*x^3+3137271*x^4+9505116*x^5+13661136*x^6+9505116*x^7+3137271*x^8+459134*x^9+25888*x^10+422*x^11+x^12)/(1-x)^15. - Bruno Berselli, Feb 08 2012

Extensions

First term added according to the formula from Bruno Berselli, Feb 08 2012
Showing 1-5 of 5 results.

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