Search: id:A137276
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%I A137276
%S A137276 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,
%T A137276 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,
%U A137276 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
%V A137276 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,
%W A137276 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,
%X A137276 -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
%N A137276 Triangle a(n,k) of coefficients [x^k] B_n(x) of the Boubaker polynomials 
               B_n(x).
%C A137276 The row-reversed version of A135929.
%C A137276 Row sums are repeating 1, 1, 3, 2, -1, -3, -2, 1, 3, 2, -1..., see A138034 
               and A119910.
%H A137276 P. Steinbach, <a href="http://www.jstor.org/stable/2691048">Golden fields: 
               a case for the heptagon</a>, Math. Mag. 70 (1997), no. 1, 22-31, 
               <a href="http://www.ams.org/mathscinet-getitem?mr=1439165">MR 1439165</
               a>
%F A137276 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.
%F A137276 B(n,x)=x*B(n-1,x)-B(n-2,x), n>4.
%F A137276 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.
%e A137276 {1}, = 1
%e A137276 {0, 1}, = x
%e A137276 {2, 0, 1}, = 2+x^2
%e A137276 {0, 1, 0, 1}, = x+x^3
%e A137276 {-2, 0, 0, 0, 1}, = -2+x^4
%e A137276 {0, -3, 0, -1, 0, 1}, = -3x-x^3+x^5
%e A137276 {2, 0, -3, 0, -2, 0, 1},
%e A137276 {0, 5, 0, -2, 0, -3, 0, 1},
%e A137276 {-2, 0, 8, 0, 0, 0, -4, 0, 1},
%e A137276 {0, -7, 0, 10, 0, 3, 0, -5, 0, 1},
%e A137276 {2, 0, -15, 0, 10, 0, 7, 0, -6, 0, 1},
%e A137276 {0, 9, 0, -25, 0, 7, 0, 12, 0, -7, 0, 1}
%p A137276 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:
%p A137276 seq( seq(A137276(n,k),k=0..n),n=0..13) ;
%Y A137276 Cf. A123956, A137289.
%Y A137276 Sequence in context: A083889 A127523 A116927 this_sequence A140581 A137277 
               A039975
%Y A137276 Adjacent sequences: A137273 A137274 A137275 this_sequence A137277 A137278 
               A137279
%K A137276 sign,tabl
%O A137276 0,4
%A A137276 Roger L. Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Mar 13 
               2008
%E A137276 Fourth row inserted by the Associate Editors of the OEIS, Aug 27 2009

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