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 32 results. Next

A113345 Matrix square of triangle A113340.

Original entry on oeis.org

1, 2, 1, 5, 6, 1, 19, 39, 10, 1, 113, 327, 105, 14, 1, 966, 3556, 1315, 203, 18, 1, 10958, 48659, 19875, 3367, 333, 22, 1, 156700, 812462, 357860, 64750, 6867, 495, 26, 1, 2727794, 16136404, 7547602, 1435497, 160005, 12199, 689, 30, 1
Offset: 0

Views

Author

Paul D. Hanna, Nov 08 2005

Keywords

Comments

Transforms column k of triangle A113340 into column k+1 of A113340. Also transforms column k of triangle A113350 into column k+1 of A113350.

Examples

			Matrix square A113340^2 starts:
1;
2,1;
5,6,1;
19,39,10,1;
113,327,105,14,1;
966,3556,1315,203,18,1;
10958,48659,19875,3367,333,22,1;
156700,812462,357860,64750,6867,495,26,1;
2727794,16136404,7547602,1435497,160005,12199,689,30,1; ...
		

Crossrefs

Cf. A113340, A113346 (column 0), A113347 (column 1), A113348 (column 2), A113349 (column 3); A113350.

Programs

  • PARI
    T(n,k)=local(A,B);A=matrix(1,1);A[1,1]=1;for(m=2,n+1,B=matrix(m,m); for(i=1,m, for(j=1,i,if(i<3 || j==i || j>m-1,B[i,j]=1,if(j==1, B[i,1]=1,B[i,j]=(A^(2*j-1))[i-j+1,1]));));A=B);(A^2)[n+1,k+1]

A113360 Matrix cube of triangle A113340.

Original entry on oeis.org

1, 3, 1, 12, 9, 1, 69, 81, 15, 1, 560, 879, 210, 21, 1, 6059, 11739, 3285, 399, 27, 1, 83215, 190044, 59395, 8127, 648, 33, 1, 1399161, 3654814, 1241270, 184436, 16245, 957, 39, 1, 28020221, 81947221, 29720808, 4695719, 442890, 28479, 1326, 45, 1
Offset: 0

Views

Author

Paul D. Hanna, Nov 08 2005

Keywords

Examples

			Triangle begins:
1;
3,1;
12,9,1;
69,81,15,1;
560,879,210,21,1;
6059,11739,3285,399,27,1;
83215,190044,59395,8127,648,33,1;
1399161,3654814,1241270,184436,16245,957,39,1;
28020221,81947221,29720808,4695719,442890,28479,1326,45,1; ...
		

Crossrefs

Cf. A113340, A113350, A113361 (column 1), A113362 (column 2), A113363 (column 3), A113364 (column 4); A113345 (A113340^2).

Programs

  • PARI
    T(n,k)=local(A,B);A=matrix(1,1);A[1,1]=1;for(m=2,n+1,B=matrix(m,m); for(i=1,m, for(j=1,i,if(i<3 || j==i || j>m-1,B[i,j]=1,if(j==1, B[i,1]=1,B[i,j]=(A^(2*j-1))[i-j+1,1]));));A=B);(A^3)[n+1,k+1]

A113341 Column 1 of triangle A113340, also equals column 0 of A113340^3.

Original entry on oeis.org

1, 3, 12, 69, 560, 6059, 83215, 1399161, 28020221, 654110586, 17494347067, 528556017365, 17830841841940, 665126088764191, 27208111182653865, 1211942062741823574, 58424831462907214924, 3031993693950136247986
Offset: 0

Views

Author

Paul D. Hanna, Nov 08 2005

Keywords

Crossrefs

Cf. A113342 (column 2), A113343 (column 3), A113344 (column 4), A113340, A113360 (=A113340^3).

Programs

  • PARI
    a(n)=local(A,B);A=matrix(1,1);A[1,1]=1;for(m=2,n+2,B=matrix(m,m); for(i=1,m, for(j=1,i,if(i<3 || j==i || j>m-1,B[i,j]=1,if(j==1, B[i,1]=1,B[i,j]=(A^(2*j-1))[i-j+1,1]));));A=B);A[n+2,2]

A113342 Column 2 of triangle A113340, also equals column 0 of A113340^5.

Original entry on oeis.org

1, 5, 35, 325, 3880, 57560, 1030751, 21763632, 531604250, 14789895891, 462672349092, 16100666809097, 617634167482824, 25916099832677757, 1181568927574816310, 58194225186901919790, 3080529680131892318877
Offset: 0

Views

Author

Paul D. Hanna, Nov 08 2005

Keywords

Crossrefs

Cf. A113341 (column 1), A113343 (column 3), A113344 (column 4), A113340.

Programs

  • PARI
    a(n)=local(A,B);A=matrix(1,1);A[1,1]=1;for(m=2,n+3,B=matrix(m,m); for(i=1,m, for(j=1,i,if(i<3 || j==i || j>m-1,B[i,j]=1,if(j==1, B[i,1]=1,B[i,j]=(A^(2*j-1))[i-j+1,1]));));A=B);A[n+3,3]

A113343 Column 3 of triangle A113340, also equals column 0 of A113340^7.

Original entry on oeis.org

1, 7, 70, 889, 13853, 258146, 5633264, 141487178, 4031806898, 128792484219, 4565493788191, 178051324792642, 7583098790779316, 350435514388561567, 17474323210108996497, 935597107908721785211, 53553176933223851350863
Offset: 0

Views

Author

Paul D. Hanna, Nov 08 2005

Keywords

Crossrefs

Cf. A113341 (column 1), A113342 (column 2), A113344 (column 4), A113340.

Programs

  • PARI
    a(n)=local(A,B);A=matrix(1,1);A[1,1]=1;for(m=2,n+4,B=matrix(m,m); for(i=1,m, for(j=1,i,if(i<3 || j==i || j>m-1,B[i,j]=1,if(j==1, B[i,1]=1,B[i,j]=(A^(2*j-1))[i-j+1,1]));));A=B);A[n+4,4]

A113344 Column 4 of triangle A113340, also equals column 0 of A113340^9.

Original entry on oeis.org

1, 9, 117, 1881, 36051, 805875, 20661609, 599319747, 19443585048, 698723462022, 27583235473854, 1187660855613822, 55430739480692085, 2789074498460404927, 150571050665946174760, 8684625004973955639293, 533144024633105768180154
Offset: 0

Views

Author

Paul D. Hanna, Nov 08 2005

Keywords

Crossrefs

Cf. A113341 (column 1), A113342 (column 2), A113343 (column 3), A113340.

Programs

  • PARI
    a(n)=local(A,B);A=matrix(1,1);A[1,1]=1;for(m=2,n+5,B=matrix(m,m); for(i=1,m, for(j=1,i,if(i<3 || j==i || j>m-1,B[i,j]=1,if(j==1, B[i,1]=1,B[i,j]=(A^(2*j-1))[i-j+1,1]));));A=B);A[n+5,5]

A113351 Column 1 of triangle A113350, also equals column 0 of A113340^4.

Original entry on oeis.org

1, 4, 22, 166, 1671, 21510, 341463, 6496923, 144856710, 3716746006, 108133664181, 3523951953981, 127331488458476, 5057405619797317, 219179491109978660, 10298771194610350427, 521765883689616772731, 28363341834962918344084
Offset: 0

Views

Author

Paul D. Hanna, Nov 08 2005

Keywords

Crossrefs

Cf. A113340, A113350, A113346 (column 0), A113352 (column 2), A113353 (column 3), A113354 (column 4).

Programs

  • PARI
    a(n)=local(A,B);A=matrix(1,1);A[1,1]=1;for(m=2,n+1,B=matrix(m,m); for(i=1,m, for(j=1,i,if(i<3 || j==i || j>m-1,B[i,j]=1,if(j==1, B[i,1]=1,B[i,j]=(A^(2*j-1))[i-j+1,1]));));A=B);(A^4)[n+1,1]

A113352 Column 2 of triangle A113350, also equals column 0 of A113340^6.

Original entry on oeis.org

1, 6, 51, 561, 7726, 129406, 2572892, 59525136, 1576414408, 47144606666, 1574176301192, 58126182666796, 2354183194432226, 103850488571214174, 4959424774062415780, 255032863135423053615, 14056171975717324065788
Offset: 0

Views

Author

Paul D. Hanna, Nov 08 2005

Keywords

Crossrefs

Cf. A113340, A113350, A113346 (column 0), A113351 (column 1), A113353 (column 3), A113354 (column 4).

Programs

  • PARI
    a(n)=local(A,B);A=matrix(1,1);A[1,1]=1;for(m=2,n+1,B=matrix(m,m); for(i=1,m, for(j=1,i,if(i<3 || j==i || j>m-1,B[i,j]=1,if(j==1, B[i,1]=1,B[i,j]=(A^(2*j-1))[i-j+1,1]));));A=B);(A^6)[n+1,1]

A113353 Column 3 of triangle A113350, also equals column 0 of A113340^8.

Original entry on oeis.org

1, 8, 92, 1324, 23010, 471724, 11198006, 303137822, 9239501237, 313689623136, 11755195387720, 482435619984340, 21537360479898341, 1039758627381190676, 54002918637393187687, 3003770445258147527669, 178205904321326719715551
Offset: 0

Views

Author

Paul D. Hanna, Nov 08 2005

Keywords

Crossrefs

Cf. A113340, A113350, A113346 (column 0), A113351 (column 1), A113352 (column 2), A113354 (column 4).

Programs

  • PARI
    a(n)=local(A,B);A=matrix(1,1);A[1,1]=1;for(m=2,n+1,B=matrix(m,m); for(i=1,m, for(j=1,i,if(i<3 || j==i || j>m-1,B[i,j]=1,if(j==1, B[i,1]=1,B[i,j]=(A^(2*j-1))[i-j+1,1]));));A=B);(A^8)[n+1,1]

A113354 Column 4 of triangle A113350, also equals column 0 of A113340^10.

Original entry on oeis.org

1, 10, 145, 2575, 53935, 1305070, 35924902, 1111107544, 38212134595, 1448428857802, 60055380515614, 2705916453572344, 131733359512179916, 6894586916062176161, 386203389346756538342, 23061963945353367894173
Offset: 0

Views

Author

Paul D. Hanna, Nov 08 2005

Keywords

Crossrefs

Cf. A113340, A113350, A113346 (column 0), A113351 (column 1), A113352 (column 2), A113353 (column 3).

Programs

  • PARI
    a(n)=local(A,B);A=matrix(1,1);A[1,1]=1;for(m=2,n+1,B=matrix(m,m); for(i=1,m, for(j=1,i,if(i<3 || j==i || j>m-1,B[i,j]=1,if(j==1, B[i,1]=1,B[i,j]=(A^(2*j-1))[i-j+1,1]));));A=B);(A^10)[n+1,1]
Showing 1-10 of 32 results. Next