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 A145462 Eigentriangle, row sums = the Padovan sequence, A000931 1
 1, 1, 1, -1, 1, 2, 0, -1, 2, 2, 1, 0, -2, 2, 3, -1, 1, 0, -2, 3, 4, 0, -1, 2, 0, -3, 4, 5, 1, 0, -2, 2, 0, -4, 5, 7, -1, 1, 0, -2, 3, 0, -5, 7, 9, 0, -1, 2, 0, -3, 4, 0, -7, 9, 12, 1, 0, -2, 2, 0, -4, 5, 0, -9, 12, 16, -1, 1, 0, -2, 3, 0, -5, 7, 0, -12, 16, 21 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 6,6 COMMENTS Right border = Padovan sequence starting with offset 6. Row sums = Padovan sequence starting with offset 7. Sum of n-th row terms = rightmost term of next row. LINKS FORMULA Triangle read by rows, T(n,k) = M * (A000931 * 0^(n-k)). M = an infinite lower triangular matrix with A106510 in every column: (1, 1, -1, 0, 1, -1, 0, 1, -1,...); and A000931 is a diagonalized infinite lower triangular matrix with the Padovan sequence starting with offset 6: (1, 1, 2, 2, 3, 4, 5, 7, 9,...) as the main diagonal and the rest zeros. EXAMPLE First few rows of the triangle = 1; 1, 1; -1, 1, 2; 0, -1, 2, 2; 1, 0, -2, 2, 3; -1, 1, 0, -2, 3, 4; 0, -1, 2, 0, -3, 4, 5; 1, 0, -2, 2, 0, -4, 5, 7; -1, 1, 0, -2, 3, 0, -5, 7, 9; 0, -1, 2, 0, -3, 4, 0, -7, 9, 12; 1, 0, -2, 2, 0, -4, 5, 0, -9, 12, 16; ... Example: Row 10 = (1, 0, -2, 2, 3) with A000931(10) = 3, rightmost term. This row = the termwise products of ((1, 0, -1, 1, 1) and (1, 1, 2, 2, 3); where the Padovan sequence starting with offset 6 = (1, 1, 2, 2, 3, 4, 5, 7, 9,...). CROSSREFS Sequence in context: A110249 A160756 A176239 * A159934 A067460 A159855 Adjacent sequences:  A145459 A145460 A145461 * A145463 A145464 A145465 KEYWORD eigen,tabl,sign AUTHOR Gary W. Adamson, Oct 10 2008 STATUS approved

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