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.

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]

A113361 Column 1 of triangle A113360, which equals the matrix cube of triangle A113340.

Original entry on oeis.org

1, 9, 81, 879, 11739, 190044, 3654814, 81947221, 2107962168, 61366149296, 1998607800064, 72112467306074, 2858551691428042, 123596917897265255, 5792708223233376744, 292682081981049699408, 15865848522184194142469
Offset: 0

Views

Author

Paul D. Hanna, Nov 08 2005

Keywords

Crossrefs

Cf. A113340, A113350, A113360 (A113340^3), A113341 (column 0), A113362 (column 2), A113363 (column 3), A113364 (column 4).

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^3)[n+2,2]

A113362 Column 2 of triangle A113360, also equals column 1 of A113340^5.

Original entry on oeis.org

1, 15, 210, 3285, 59395, 1241270, 29720808, 806720492, 24568601477, 831697990069, 31036137984664, 1267376997249262, 56270606942915489, 2701018385881136958, 139463341982980040911, 7711492696761363573725
Offset: 0

Views

Author

Paul D. Hanna, Nov 08 2005

Keywords

Comments

A113360 equals the matrix cube of triangle A113340, where column 2 of A113340^3 = column 1 of A113340^5.

Crossrefs

Cf. A113340, A113350, A113360 (A113340^3), A113341 (column 0), A113361 (column 1), A113363 (column 3), A113364 (column 4).

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^3)[n+3,3]

A113363 Column 3 of triangle A113360, also equals column 1 of A113340^7.

Original entry on oeis.org

1, 21, 399, 8127, 184436, 4695719, 133730310, 4234560596, 148077895854, 5680484146379, 237574859841676, 10771591113205720, 526750324271281348, 27655229128194306702, 1552379671658643163707, 92820542631741826797326
Offset: 0

Views

Author

Paul D. Hanna, Nov 08 2005

Keywords

Comments

A113360 equals the matrix cube of triangle A113340, where column 3 of A113340^3 = column 1 of A113340^7.

Crossrefs

Cf. A113340, A113350, A113360 (A113340^3), A113341 (column 0), A113361 (column 1), A113362 (column 2), A113364 (column 4).

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^3)[n+4,4]

A116988 Sum of digits of (10^n)!.

Original entry on oeis.org

1, 27, 648, 10539, 149346, 1938780, 23903442, 284222502, 3292100235, 37420852599
Offset: 0

Views

Author

Zak Seidov, Apr 02 2006

Keywords

Comments

Cf. A004152 Sum of digits of factorial numbers, A113364 1,27,648,16245,... with first three terms coinciding with this SEQ.

Examples

			a(1)=27 because 10!=3628800 and 3+6+2+8+8+0+0=27.
		

Crossrefs

Programs

  • Mathematica
    Do[Print[Total[IntegerDigits[(10^n)! ]]], {n, 0, 7}]
  • Python
    from math import factorial
    def A116988(n):
        return sum(int(d) for d in str(factorial(10**n))) # Chai Wah Wu, May 21 2018

Extensions

One more term from Ryan Propper, Jun 27 2007
a(9) from Chai Wah Wu, May 21 2018
Showing 1-5 of 5 results.