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Search: id:A136238
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| 1, 9, 1, 99, 18, 1, 1323, 306, 27, 1, 21036, 5643, 621, 36, 1, 390012, 115917, 14580, 1044, 45, 1, 8287041, 2657946, 366129, 29754, 1575, 54, 1, 198918840, 67708113, 9968067, 882318, 52785, 2214, 63, 1, 5329794042, 1903562412, 294952140
(list; table; graph; listen)
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OFFSET
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0,2
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FORMULA
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Column k of W^3 (this triangle) = column 2 of W^(k+1), where W = P^3 and P = triangle A136220.
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EXAMPLE
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This triangle, W^3, begins:
1;
9, 1;
99, 18, 1;
1323, 306, 27, 1;
21036, 5643, 621, 36, 1;
390012, 115917, 14580, 1044, 45, 1;
8287041, 2657946, 366129, 29754, 1575, 54, 1;
198918840, 67708113, 9968067, 882318, 52785, 2214, 63, 1;
5329794042, 1903562412, 294952140, 27779046, 1804290, 85293, 2961, 72, 1;
where column 0 of W^3 = column 2 of W = triangle A136231.
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PROGRAM
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(PARI) {T(n, k)=local(P=Mat(1), U=Mat(1), W=Mat(1), PShR); if(n>0, for(i=0, n, PShR=matrix(#P, #P, r, c, if(r>=c, if(r==c, 1, if(c==1, 0, P[r-1, c-1])))); U=P*PShR^2; U=matrix(#P+1, #P+1, r, c, if(r>=c, if(r<#P+1, U[r, c], if(c==1, (P^3)[ #P, 1], (P^(3*c-1))[r-c+1, 1])))); P=matrix(#U, #U, r, c, if(r>=c, if(r<#R, P[r, c], (U^c)[r-c+1, 1]))); W=P^3; )); (W^3)[n+1, k+1]}
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CROSSREFS
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Cf. related tables: A136220 (P), A136228 (U), A136230 (V), A136231 (W), A136235 (W^2).
Adjacent sequences: A136235 A136236 A136237 this_sequence A136239 A136240 A136241
Sequence in context: A138342 A101678 A051380 this_sequence A113394 A051231 A046761
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Feb 07 2008
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