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A145468
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Convolution square of A003106.
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1
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1, 0, 2, 2, 3, 4, 7, 8, 13, 16, 23, 28, 40, 48, 66, 82, 107, 132, 171, 208, 266, 324, 406, 494, 614, 740, 912, 1098, 1338, 1604, 1945, 2318, 2793, 3320, 3972, 4706, 5605, 6612, 7840, 9222, 10882, 12760, 15004, 17534, 20542, 23944, 27949, 32490, 37813, 43832
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| Expansion of H(x)^2 in powers of x where H() is a Rogers-Ramanujan function.
Euler transform of period 5 sequence [ 0, 2, 2, 0, 0, ...].
G.f.: (1 + Sum_{k>0} x^(k^2 - k) / ((1 - t) * (1 - t^2) * ... * (1 - t^k)))^2 = (Product_{k>0} (1 - x^(5*k - 2)) * (1 - x^(5*k -3)))^-2.
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EXAMPLE
| q^11 + 2*q^71 + 2*q^101 + 3*q^131 + 4*q^161 + 7*q^191 + 8*q^221 + ...
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PROG
| (PARI) {a(n) = local(t); if( n<0, 0, t = 1 + x * O(x^n); polcoeff( sum(k= 1, (sqrt(4*n + 1) - 1) / 2, t *= x^(2*k) / (1 - x^k) * (1 + x * O(x^(n - k^2 - k))), 1)^2, n))}
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CROSSREFS
| -A145466(5*n+2) = a(n).
Sequence in context: A014692 A058670 A091605 * A125554 A083130 A083129
Adjacent sequences: A145465 A145466 A145467 * A145469 A145470 A145471
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Oct 11 2008
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