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 A164981 A triangle with Pell numbers in the first column. 3
 1, 2, 1, 5, 3, 1, 12, 10, 4, 1, 29, 30, 16, 5, 1, 70, 87, 56, 23, 6, 1, 169, 245, 185, 91, 31, 7, 1, 408, 676, 584, 334, 136, 40, 8, 1, 985, 1836, 1784, 1158, 546, 192, 50, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Rows sum up to A000244 (powers of 3), diagonals to A001654 (golden rectangles). Up to reflection at the vertical axis, the triangle of numbers given here coincides with the triangle given in A210557, i.e. the numbers are the same just read row-wise in the opposite direction. [Christine Bessenrodt, Jul 20 2012] Subtriangle of (0, 2, 1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Oct 10 2013 LINKS FORMULA Excel formula: E4 = E3*2+D3+E2-D2 ; with a(1)=E3=1 and a(2)= E4 T(1,1) =1. T(n,k)=0 if n<1 or k<1 or k>n. T(n,k) = 2*T(n-1,k)+T(n-1,k-1)+T(n-2,k)-T(n-2,k-1) otherwise. - R. J. Mathar, Jan 27 2011 T(n,1) = A000129(n). T(n,n-1) = n. T(n,n-2) = A052905(n-2). - R. J. Mathar, Jan 27 2011 T(n,2) = A026937(n-2). - R. J. Mathar, Jan 27 2011 G.f. x*y/(1-2*x-x^2+x^2*y-x*y). - R. J. Mathar, Aug 11 2015 EXAMPLE 1 2,1 5,3,1 12,10,4,1 29,30,16,5,1 70,87,56,23,6,1 169,245,185,91,31,7,1 Triangle T(n,k) = (0, 2, 1/2, -1/2, 0, 0, ...) DELTA (1, 0, -1/2, 1/2, 0, 0, ...) begins (0<=k<=n) : 1 0, 1 0, 2, 1 0, 5, 3, 1 0, 12, 10, 4, 1 0, 29, 30, 16, 5, 1 0, 70, 87, 56, 23, 6, 1 0, 169, 245, 185, 91, 31, 7, 1 ... Philippe Deléham, Oct 10 2013 MAPLE A164981 := proc(n, k) option remember; if n <1 or k<1 or k>n then 0; elif n = 1 then 1; else 2*procname(n-1, k)+procname(n-1, k-1)+procname(n-2, k)-procname(n-2, k-1) ; end if; end proc: CROSSREFS Cf. A000244, A001654, A164975, A164976, A210557 Sequence in context: A130197 A106513 A054446 * A047858 A125171 A280784 Adjacent sequences:  A164978 A164979 A164980 * A164982 A164983 A164984 KEYWORD nonn,tabl AUTHOR Mark Dols, Sep 03 2009 STATUS approved

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Last modified October 15 09:22 EDT 2019. Contains 328026 sequences. (Running on oeis4.)