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Search: id:A137276
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| A137276 |
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Triangle a(n,k) of coefficients [x^k] B_n(x) of the Boubaker polynomials B_n(x). |
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+0
11
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| 1, 0, 1, 2, 0, 1, 0, 1, 0, 1, -2, 0, 0, 0, 1, 0, -3, 0, -1, 0, 1, 2, 0, -3, 0, -2, 0, 1, 0, 5, 0, -2, 0, -3, 0, 1, -2, 0, 8, 0, 0, 0, -4, 0, 1, 0, -7, 0, 10, 0, 3, 0, -5, 0, 1, 2, 0, -15, 0, 10, 0, 7, 0, -6, 0, 1, 0, 9, 0, -25, 0, 7, 0, 12, 0, -7, 0, 1, -2, 0, 24, 0, -35, 0, 0, 0, 18, 0, -8, 0, 1, 0, -11, 0, 49, 0, -42, 0, -12, 0
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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The row-reversed version of A135929.
Row sums are repeating 1, 1, 3, 2, -1, -3, -2, 1, 3, 2, -1..., see A138034 and A119910.
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LINKS
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P. Steinbach, Golden fields: a case for the heptagon, Math. Mag. 70 (1997), no. 1, 22-31, MR 1439165
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FORMULA
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a(n,k)= 0 if n-k odd. a(n,k)= 2*(-1)^((n-k)/2)*(2k-n)/(n+k)*binomial((n+k)/2,(n-k)/2) if n-k even.
B(n,x)=x*B(n-1,x)-B(n-2,x), n>4.
B(n,2*x)= -2*T(n,x)+4*x*U(n-1,x), where T(n,x) is A053120 and U(n,x) is A053117.
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EXAMPLE
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{1}, = 1
{0, 1}, = x
{2, 0, 1}, = 2+x^2
{0, 1, 0, 1}, = x+x^3
{-2, 0, 0, 0, 1}, = -2+x^4
{0, -3, 0, -1, 0, 1}, = -3x-x^3+x^5
{2, 0, -3, 0, -2, 0, 1},
{0, 5, 0, -2, 0, -3, 0, 1},
{-2, 0, 8, 0, 0, 0, -4, 0, 1},
{0, -7, 0, 10, 0, 3, 0, -5, 0, 1},
{2, 0, -15, 0, 10, 0, 7, 0, -6, 0, 1},
{0, 9, 0, -25, 0, 7, 0, 12, 0, -7, 0, 1}
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MAPLE
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A137276 := proc(n, k) local nmk, npk; if n = 0 then 1; elif (n-k) mod 2 <> 0 then 0; else nmk := (n-k)/2 ; npk := (n+k)/2 ; (-1)^nmk*(2*k-n)/npk*binomial(npk, nmk) ; fi; end:
seq( seq(A137276(n, k), k=0..n), n=0..13) ;
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CROSSREFS
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Cf. A123956, A137289.
Sequence in context: A083889 A127523 A116927 this_sequence A140581 A137277 A039975
Adjacent sequences: A137273 A137274 A137275 this_sequence A137277 A137278 A137279
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KEYWORD
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sign,tabl
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AUTHOR
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Roger L. Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Mar 13 2008
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EXTENSIONS
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Fourth row inserted by the Associate Editors of the OEIS, Aug 27 2009
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