A113346
Column 0 of triangle A113345, also equals column 0 of A113350.
Original entry on oeis.org
1, 2, 5, 19, 113, 966, 10958, 156700, 2727794, 56306696, 1350043965, 36979531549, 1141573025172, 39272377323693, 1491452150268436, 62027842189908231, 2805631215820328992, 137199563717151509077, 7215932308408758314447
Offset: 0
-
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^2)[n+1,1]
A113355
Triangle T, read by rows, equal to the matrix square of triangle A113350, where T transforms column k of T into column k+1 of T.
Original entry on oeis.org
1, 4, 1, 18, 8, 1, 112, 68, 12, 1, 965, 712, 150, 16, 1, 10957, 9270, 2184, 264, 20, 1, 156699, 147174, 37523, 4912, 410, 24, 1, 2727793, 2786270, 754171, 104476, 9280, 588, 28, 1, 56306695, 61662544, 17502145, 2531004, 235025, 15672, 798, 32, 1
Offset: 0
Triangle T begins:
1;
4,1;
18,8,1;
112,68,12,1;
965,712,150,16,1;
10957,9270,2184,264,20,1;
156699,147174,37523,4912,410,24,1;
2727793,2786270,754171,104476,9280,588,28,1;
56306695,61662544,17502145,2531004,235025,15672,798,32,1; ...
where T transforms column k of T into column k+1:
at k=0, [Q^2]*[1,4,18,112,965,...] = [1,8,68,712,9270,...];
at k=1, [Q^2]*[1,8,68,712,9270,...] = [1,12,150,2184,37523,...].
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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); (matrix(#A,#A,r,c,if(r>=c,(A^(2*c))[r-c+1,1]))^2)[n+1,k+1]
A113347
Column 1 of triangle A113345, also equals column 0 of A113350^3.
Original entry on oeis.org
1, 6, 39, 327, 3556, 48659, 812462, 16136404, 373415239, 9900007028, 296557405704, 9921937128500, 367181525916035, 14906571298831661, 659191947156441025, 31558799717042019635, 1626968083690674214906
Offset: 0
-
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^2)[n+2,2]
A113348
Column 2 of triangle A113345, also equals column 0 of A113350^5.
Original entry on oeis.org
1, 10, 105, 1315, 19875, 357860, 7547602, 183518246, 5072961513, 157525315615, 5438681986872, 206954207984234, 8613936431369952, 389602050945939891, 19038814387466399303, 1000152089409979423044, 56229083214210734799693
Offset: 0
-
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^2)[n+3,3]
A113349
Column 3 of triangle A113345, also equals column 0 of A113350^7.
Original entry on oeis.org
1, 14, 203, 3367, 64750, 1435497, 36312626, 1036877170, 33086963196, 1169366274321, 45412092740791, 1924418011638535, 88445828358934074, 4384910640997110602, 233384463606862044134, 13278878088344760573344
Offset: 0
-
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^2)[n+4,4]
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
-
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
-
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
-
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
-
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]
A113356
Column 0 of triangle A113355, which is the matrix square of A113350.
Original entry on oeis.org
1, 4, 18, 112, 965, 10957, 156699, 2727793, 56306695, 1350043964, 36979531548, 1141573025171, 39272377323692, 1491452150268435, 62027842189908230, 2805631215820328991, 137199563717151509076, 7215932308408758314446
Offset: 0
-
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); (matrix(#A,#A,r,c,if(r>=c,(A^(2*c))[r-c+1,1]))^2)[n+1,1]
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