The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A136231 Triangle W, read by rows, where column k of W = column 0 of W^(k+1) for k>=0 such that W equals the matrix cube of P = A136220 with column 0 of W = column 0 of P shift up one row. 11
 1, 3, 1, 15, 6, 1, 108, 48, 9, 1, 1036, 495, 99, 12, 1, 12569, 6338, 1323, 168, 15, 1, 185704, 97681, 21036, 2754, 255, 18, 1, 3247546, 1767845, 390012, 52204, 4950, 360, 21, 1, 65762269, 36839663, 8287041, 1128404, 108860, 8073, 483, 24, 1, 1515642725 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This triangle W is the column transform for triangles U=A136228 and V=A136230: W * [column k of U] = column k+1 of U and W * [column k of V] = column k+1 of V, for k>=0. LINKS EXAMPLE Triangle W begins: 1; 3, 1; 15, 6, 1; 108, 48, 9, 1; 1036, 495, 99, 12, 1; 12569, 6338, 1323, 168, 15, 1; 185704, 97681, 21036, 2754, 255, 18, 1; 3247546, 1767845, 390012, 52204, 4950, 360, 21, 1; 65762269, 36839663, 8287041, 1128404, 108860, 8073, 483, 24, 1; ... where column k of W = column 0 of W^(k+1) such that W = P^3 and triangle P = A136220 begins: 1; 1, 1; 3, 2, 1; 15, 10, 3, 1; 108, 75, 21, 4, 1; 1036, 753, 208, 36, 5, 1; 12569, 9534, 2637, 442, 55, 6, 1; ... where column k of P^3 = column 0 of P^(3k+3) such that column 0 of P^3 = column 0 of P shift up one row. Also, this triangle W equals the matrix product: W = V * [V shift down one row] where triangle V = A136230 begins: 1; 2, 1; 8, 5, 1; 49, 35, 8, 1; 414, 325, 80, 11, 1; 4529, 3820, 988, 143, 14, 1; 61369, 54800, 14696, 2200, 224, 17, 1; ... and V shift down one row begins: 1; 1, 1; 2, 1, 1; 8, 5, 1, 1; 49, 35, 8, 1, 1; 414, 325, 80, 11, 1, 1; 4529, 3820, 988, 143, 14, 1, 1; ... PROG (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[n+1, k+1]} CROSSREFS Cf. A136221 (column 0); related tables: A136220 (P), A136225 (P^2), A136228 (U), A136230 (V), A136235 (W^2), A136238 (W^3); A136217, A136218. Sequence in context: A297704 A104990 A089463 * A113389 A038553 A282629 Adjacent sequences:  A136228 A136229 A136230 * A136232 A136233 A136234 KEYWORD nonn,tabl AUTHOR Paul D. Hanna, Jan 28 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 27 16:20 EDT 2020. Contains 337383 sequences. (Running on oeis4.)