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A227300
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Rising diagonal sums of triangle of Fibonacci polynomials (rows displayed as centered text).
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2
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1, 2, 2, 3, 7, 11, 16, 28, 48, 77, 126, 211, 349, 573, 947, 1568, 2588, 4271, 7058, 11661, 19256, 31804, 52538, 86779, 143329, 236744, 391046, 645900, 1066850, 1762163, 2910634, 4807590, 7940870, 13116238, 21664568, 35784145, 59105987, 97627533, 161254953, 266350689
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OFFSET
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1,2
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COMMENTS
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Rising diagonal sums of triangle A011973, taken with rows as centered text.
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LINKS
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FORMULA
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a(n) = sum(k=0..floor((n-1)/3), binomial(2*n-2-5*k,k) + binomial(2*n-3-5*k,k)) for n>=2; a(1)=1. - John Molokach, Jul 11 2013
a(n) = a(n-1) + 2*a(n-3) - a(n-6), starting with {1, 2, 2, 3, 7, 11}. - T. D. Noe, Jul 11 2013
a(n) = sum(k=0..floor((2n-1)/3) binomial(2n-k-2-3*floor(k/2),floor(k/2))). - John Molokach, Jul 29 2013
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EXAMPLE
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a(1) = 1; a(2) = 1+1; a(3) = 1+1; a(4) = 1+1+1; a(5) = 1+1+3+2; a(6) = 1+1+5+4; a(7) = 1+1+7+6+1; a(8) = 1+1+9+8+6+3; a(9) = 1+1+11+10+15+10; a(10) = 1+1+13+12+28+21+1.
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MATHEMATICA
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LinearRecurrence[{1, 0, 2, 0, 0, -1}, {1, 2, 2, 3, 7, 11}, 40] (* T. D. Noe, Jul 11 2013 *)
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PROG
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(PARI) a(n) = if(n<=1, 1, sum(k=0, floor((n-1)/3), binomial(2*n-2-5*k, k)+binomial(2*n-1-5*k, k)) ); \\ Joerg Arndt, Jul 11 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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