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A154958
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Antidiagonal sums of number triangle A154957 regarded as a lower triangular infinite matrix.
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3
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1, 1, 2, 1, 2, 1, 3, 2, 4, 2, 4, 2, 5, 3, 6, 3, 6, 3, 7, 4, 8, 4, 8, 4, 9, 5, 10, 5, 10, 5, 11, 6, 12, 6, 12, 6, 13, 7, 14, 7, 14, 7, 15, 8, 16, 8, 16, 8, 17, 9, 18, 9, 18, 9, 19, 10, 20, 10, 20, 10, 21, 11, 22, 11, 22, 11, 23, 12, 24, 12, 24, 12, 25, 13, 26, 13, 26, 13, 27, 14, 28, 14, 28
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = a(n-1) + a(n-2) - 2*a(n-3) + a(n-4) + a(n-5) - a(n-6), a(0) = 1, a(1) = 1, a(2) = 2, a(3) = 1, a(4) = 2, a(5) = 1. - Philippe Deléham, Mar 21 2014
Euler transform of length 6 sequence [ 1, 1, -1, 0, 0, 1]. - Michael Somos, Mar 21 2014
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EXAMPLE
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G.f. = 1 + x + 2*x^2 + x^3 + 2*x^4 + x^5 + 3*x^6 + 2*x^7 + 4*x^8 + 2*x^9 + ...
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MATHEMATICA
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CoefficientList[Series[1/((x - 1)^2 (x + 1)^2 (x^2 - x + 1)), {x, 0, 100}], x] (* Vincenzo Librandi, Mar 22 2014 *)
LinearRecurrence[{1, 1, -2, 1, 1, -1}, {1, 1, 2, 1, 2, 1}, 90] (* Harvey P. Dale, Aug 26 2016 *)
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PROG
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(PARI) {a(n) = if( n<-5, -a(-6-n), if( n<0, 0, polcoeff( 1 / (1 - x - x^2 + 2*x^3 - x^4 - x^5 + x^6) + x * O(x^n), n)))}; /* Michael Somos, Mar 21 2014 */
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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