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Search: id:A099589
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| A099589 |
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Expansion of x^3 / (1 - 4x + 6x^2 - 4x^3 + 2x^4). |
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+0
4
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| 0, 0, 1, 4, 10, 20, 34, 48, 48, 0, -164, -560, -1352, -2704, -4616, -6528, -6528, 0, 22288, 76096, 183712, 367424, 627232, 887040, 887040, 0, -3028544, -10340096, -24963200, -49926400, -85229696, -120532992, -120532992, 0, 411525376
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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G.f. is x^3/((1+x)^4+x^4), the binomial transform of x^3/(1+x^4). - Paul Barry (pbarry(AT)wit.ie), Apr 01 2005
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LINKS
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G. Tollisen and T. Lengyel, A congruential identity ..., Integers 4 (2004), #A4.
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FORMULA
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Coefficient of x^3 in (1+x)^n mod 1+x^4.
a(n)=(2-sqrt(2))^(n/2)(sqrt(2)cos(3*pi*n/8)/4+sqrt(2)sin(3*pi*n/8)/4)+ (2+sqrt(2))^(n/2)(sqrt(2)*sin(pi*n/8)/4-sqrt(2)cos(pi*n/8)/4) - Paul Barry (pbarry(AT)wit.ie), Apr 01 2005
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PROGRAM
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(PARI) a(n) = polcoeff(((1+x)^n)%(x^4+1), 1)
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CROSSREFS
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Cf. A099586, A099587, A099588.
Sequence in context: A008045 A008124 A019457 this_sequence A008141 A119651 A005893
Adjacent sequences: A099586 A099587 A099588 this_sequence A099590 A099591 A099592
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KEYWORD
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sign
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AUTHOR
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Ralf Stephan, Oct 24 2004
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