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 A292789 Triangle read by rows: T(n,k) = (-3)*T(n-1,k-1) + T(n,k-1) with T(2*m,0) = 0 and T(2*m+1,0) = (-2)^m. 3
 0, 1, 1, 0, -3, -6, -2, -2, 7, 25, 0, 6, 12, -9, -84, 4, 4, -14, -50, -23, 229, 0, -12, -24, 18, 168, 237, -450, -8, -8, 28, 100, 46, -458, -1169, 181, 0, 24, 48, -36, -336, -474, 900, 4407, 3864, 16, 16, -56, -200, -92, 916, 2338, -362, -13583, -25175, 0, -48 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Seiichi Manyama, Rows n = 0..139, flattened FORMULA T(n+1,n)^2 + 2*T(n,n)^2 = 11^n. EXAMPLE First few rows are: 0; 1, 1; 0, -3, -6; -2, -2, 7, 25; 0, 6, 12, -9, -84; 4, 4, -14, -50, -23, 229; 0, -12, -24, 18, 168, 237, -450; -8, -8, 28, 100, 46, -458, -1169, 181; 0, 24, 48, -36, -336, -474, 900, 4407, 3864. -------------------------------------------------------------- The diagonal is {0, 1, -6, 25, -84, ...} and the next diagonal is {1, -3, 7, -9, -23, ...}. Two sequences have the following property: 1^2 + 2* 0^2 = 1 (= 11^0), (-3)^2 + 2* 1^2 = 11 (= 11^1), 7^2 + 2* (-6)^2 = 121 (= 11^2), (-9)^2 + 2* 25^2 = 1331 (= 11^3), (-23)^2 + 2*(-84)^2 = 14641 (= 11^4), ... CROSSREFS T(n,k) = b*T(n-1,k-1) + T(n,k-1): this sequence (b=-3), A292495 (b=-2), A117918 and A228405 (b=1), A227418 (b=2), A292466 (b=4). Sequence in context: A120907 A133358 A058099 * A124085 A132120 A021280 Adjacent sequences: A292786 A292787 A292788 * A292790 A292791 A292792 KEYWORD sign,tabl AUTHOR Seiichi Manyama, Sep 23 2017 STATUS approved

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Last modified February 3 21:17 EST 2023. Contains 360045 sequences. (Running on oeis4.)