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A024458
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a(n) = s(1)s(n) + s(2)s(n-1) + ... + s(k)s(n+1-k), where k = [ (n+1)/2 ], s = (Fibonacci numbers).
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2
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1, 1, 3, 5, 12, 19, 40, 65, 130, 210, 404, 654, 1227, 1985, 3653, 5911, 10720, 17345, 31090, 50305, 89316, 144516, 254568, 411900, 720757, 1166209, 2029095, 3283145, 5684340, 9197455, 15855964, 25655489, 44061862, 71293590, 122032508
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Contribution from Wolfdieter Lang, Jan 02 2012 (Start)
chat(n):=a(n+1), n>=0, is the half-convolution of the sequence A000045(n+1), n>=0, with itself. For the definition of half-convolution see a comment on A201204, where also the rule to find the o.g.f. is given. Here the o.g.f. is obtained from (U(x)^2 + U2(x^2))/2 with U(x)=1/(1-x-x^2),the o.g.f. of A000045(n+1), n>=0, and U2(x):=(1-x)/((1+x)*(1-3*x+x^2) the o.g.f. of A007598(n+1), n>=0. This coincides with the o.g.f. given below in the formula section after x has been divided.
For the bisection of this half-convolution see A027991(n+1) and A001870(n), n>=0.
(End)
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FORMULA
| G.f.: x(x^3-x^2+1)/[(1+x^2)(1+x-x^2)(1-x-x^2)^2].
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CROSSREFS
| Sequence in context: A198301 A082740 A010067 * A143643 A089292 A143360
Adjacent sequences: A024455 A024456 A024457 * A024459 A024460 A024461
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 03 2000
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