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 A105535 Triangular matrix T, read by rows, where diagonal n equals T^(n+1) when flattened (as read by rows), for n>=0. 4
 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 4, 1, 4, 2, 1, 5, 1, 9, 4, 1, 1, 6, 1, 16, 6, 1, 1, 1, 7, 1, 25, 8, 1, 6, 3, 1, 8, 1, 36, 10, 1, 17, 8, 1, 1, 9, 1, 49, 12, 1, 36, 15, 2, 1, 1, 10, 1, 64, 14, 1, 65, 24, 3, 1, 1, 1, 11, 1, 81, 16, 1, 106, 35, 4, 1, 12, 4, 1, 12, 1, 100, 18, 1, 161, 48, 5, 1, 61, 26 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS The ratio of consecutive row sums seems to converge to a value near 2, but it is not yet certain that the limit exists. LINKS Table of n, a(n) for n=0..89. EXAMPLE Triangle begins: 1; 1,1; 1,2,1; 1,3,1,1; 1,4,1,4,2; 1,5,1,9,4,1; 1,6,1,16,6,1,1; 1,7,1,25,8,1,6,3; 1,8,1,36,10,1,17,8,1; 1,9,1,49,12,1,36,15,2,1; 1,10,1,64,14,1,65,24,3,1,1; ... which when flattened (read by rows) forms diagonal 0: 1,1,1,1,2,1,1,3,1,1,1,4,1,4,2,1,5,1,9,4,1,... The matrix square, T^2 = A105537, begins: 1; 2,1; 4,4,1; 6,8,2,1; 12,26,7,12,4; ... which when flattened (read by rows) forms diagonal 1: 1,2,1,4,4,1,6,8,2,1,12,26,7,12,4,... The matrix cube, T^3 = A105539, begins: 1; 3,1; 9,6,1; 17,15,3,1; 61,92,23,28,8; ... which when flattened (read by rows) forms diagonal 2: 1,3,1,9,6,1,17,15,3,1,61,92,23,28,8,... PROG (PARI) {T(n, k)=local(A=matrix(n+1, n+1, r, c, if(r>=c, 1)), B, TK=floor((sqrt(8*k+1)-1)/2), TC); B=A; for(r=0, n, for(c=0, r, TC=floor((sqrt(8*c+1)-1)/2); B[r+1, c+1]=(A^(r-c+1))[TC+1, c-TC*(TC+1)/2+1]); A=B); return((A^(n-k+1))[TK+1, k-TK*(TK+1)/2+1])} CROSSREFS Cf. A105536 (row sums), A105537 (matrix square), A105539 (matrix cube). Sequence in context: A334215 A164823 A167269 * A182980 A244051 A207974 Adjacent sequences: A105532 A105533 A105534 * A105536 A105537 A105538 KEYWORD nonn,tabl AUTHOR Paul D. Hanna, Apr 12 2005 STATUS approved

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Last modified August 8 13:58 EDT 2024. Contains 375021 sequences. (Running on oeis4.)