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1, 6, 17, 33, 54, 81, 114, 152, 195, 244, 298, 357, 422, 492, 567, 648, 735, 827, 924, 1027, 1135, 1248, 1367, 1491, 1620, 1755, 1896, 2042, 2193, 2350, 2512, 2679, 2852, 3030, 3213, 3402, 3597, 3797, 4002, 4213, 4429, 4650, 4877, 5109, 5346, 5589, 5838, 6092, 6351, 6616, 6886, 7161, 7442, 7728, 8019, 8316, 8619, 8927
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OFFSET
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0,2
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COMMENTS
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Linear recurrence and g.f. confirmed by Shutov/Maleev link in A301726. - Ray Chandler, Aug 30 2023
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (3, -4, 4, -4, 4, -4, 4, -4, 4, -3, 1).
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FORMULA
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G.f.: (1 + x + x^2)*(1 + 2*x + 3*x^4 + 2*x^7 + x^8) / ((1 - x)^3*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)).
a(n) = 3*a(n-1) - 4*a(n-2) + 4*a(n-3) - 4*a(n-4) + 4*a(n-5) - 4*a(n-6) + 4*a(n-7) - 4*a(n-8) + 4*a(n-9) - 3*a(n-10) + a(n-11) for n>10.
(End)
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MATHEMATICA
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Accumulate[CoefficientList[Series[(x^2+x+1)(x^8+2x^7+3x^4+2x+1)/ ((x^4+ x^3+x^2+x+1)(x^4-x^3+x^2-x+1)(x-1)^2), {x, 0, 110}], x]] (* Harvey P. Dale, Sep 25 2020 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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