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Search: id:A136389
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| A136389 |
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Triangle read by rows of coefficients of Chebyshev-like polynomials P_{n,3}(x) with 0 omitted (exponents in increasing order). |
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+0
1
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| 1, -3, 2, 3, -7, 4, -1, 9, -16, 8, -5, 25, -36, 16, 1, -19, 66, -80, 32, 7, -63, 168, -176, 64, -1, 33, -192, 416, -384, 128, -9, 129, -552, 1008, -832, 256, 1, -51, 450, -1520, 2400, -1792, 512, 11, -231, 1452, -4048, 5632, -3840, 1024, -1, 73, -912, 4424, -10496, 13056, -8192, 2048
(list; graph; listen)
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OFFSET
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3,2
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COMMENT
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If U_n(x), T_n(x) are Chebyshev's polynomials then U_n(x)=P_{n,0}(x), T_n(x)=P_{n,1}(x).
Let n>=3 and k be of the same parity. Consider a set X consisting of (n+k)/2-3 blocks of the size 2 and an additional block of the size 3, then (-1)^((n-k)/2)a(n,k) is the number of n-3-subsets of X intersecting each block of the size 2.
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LINKS
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Milan Janjic, Two enumerative functions.
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FORMULA
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If n>=3 and k are of the same parity then a(n,k)= (-1)^((n-k)/2)*sum((-1)^i*binomial((n+k)/2-3, i)*binomial(n+k-3-2*i, n-3), i=0..(n+k)/2-3), and a(n,k)=0 if n and k are of different parity.
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EXAMPLE
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Rows are (1),(-3,2),(3,-7,4),(-1,0,-16,8),...
since P_{3,3}=x^3, P_{4,3}=-3x^2+2x^4, P_{5,3}=3x-7x^3+4x^5,...
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MAPLE
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if modp(n-k, 2)=0 then a[n, k]:=(-1)^((n-k)/2)*sum((-1)^i*binomial((n+k)/2-3, i)*binomial(n+k-3-2*i, n-3), i=0..(n+k)/2-3); end if;
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CROSSREFS
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Cf. A008310, A053117.
Adjacent sequences: A136386 A136387 A136388 this_sequence A136390 A136391 A136392
Sequence in context: A049923 A007054 A084388 this_sequence A001368 A071010 A073341
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KEYWORD
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sign
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AUTHOR
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Milan R. Janjic (agnus(AT)blic.net), Mar 30 2008, revised Apr 05 2008
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