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A099491
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A Chebyshev transform of Padovan numbers.
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0
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1, 0, 0, 1, -1, -2, 2, 1, -4, 3, 6, -10, -3, 19, -12, -24, 43, 8, -83, 56, 100, -187, -21, 354, -262, -411, 820, 39, -1506, 1210, 1673, -3593, 56, 6400, -5545, -6768, 15705, -1216, -27144, 25273, 27207, -68490, 9442, 114857, -114644, -108565, 298054, -58738, -484827, 517803, 429452, -1294392, 330499
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| A Chebyshev transform of A000931(n+3), which has g.f. 1/(1-x^2-x^3). The image of G(x) under the Chebyshev transform is (1/(1+x^2))G(x/(1+x^2)).
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FORMULA
| G.f.: (1+x^2)^2/(1+2x^2-x^3+2x^4+x^6); a(n)=-2a(n-2)+a(n-3)-2a(n-4)-a(n-6); a(n)=sum{k=0..floor(n/2), C(n-k, k)(-1)^k*sum{j=0..floor((n-2k)/2), C(j, n-2k-2j)}}.
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CROSSREFS
| Cf. A099492.
Sequence in context: A177424 A129903 A023616 * A129862 A138189 A110090
Adjacent sequences: A099488 A099489 A099490 * A099492 A099493 A099494
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KEYWORD
| easy,sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Oct 19 2004
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