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A227376
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G.f.: 1/(1 - x - x^2 - x^3 + x^5 + x^6 + x^7).
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1
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1, 1, 2, 4, 7, 12, 21, 36, 62, 106, 181, 309, 527, 898, 1530, 2606, 4438, 7557, 12867, 21907, 37297, 63497, 108100, 184032, 313298, 533359, 907988, 1545751, 2631469, 4479778, 7626309, 12982911, 22101900, 37625912, 64053725, 109043981, 185634620, 316021206, 537989084, 915863373
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OFFSET
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0,3
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COMMENTS
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Compare to sequence A227375, generated by a continued fraction.
Lim_{n->infinity} a(n)/a(n+1) = 0.587411973105598587998520092901249815195963...
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LINKS
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Table of n, a(n) for n=0..39.
Index entries for linear recurrences with constant coefficients, signature (1,1,1,0,-1,-1,-1).
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FORMULA
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a(n) = a(n-1) + a(n-2) + a(n-3) - a(n-5) - a(n-6) - a(n-7). - Wesley Ivan Hurt, May 22 2021
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EXAMPLE
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G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 5*x^5 + 9*x^6 + 14*x^7 + 24*x^8 + ...
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MATHEMATICA
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CoefficientList[Series[1/(1-x-x^2-x^3+x^5+x^6+x^7), {x, 0, 50}], x] (* Harvey P. Dale, Mar 09 2021 *)
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PROG
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(PARI) {a(n)=polcoeff(1/(1 - x - x^2 - x^3 + x^5 + x^6 + x^7 +x*O(x^n)), n)}
for(n=0, 50, print1(a(n), ", "))
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CROSSREFS
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Cf. A227375.
Sequence in context: A094974 A306306 A357947 * A245531 A189593 A100671
Adjacent sequences: A227373 A227374 A227375 * A227377 A227378 A227379
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KEYWORD
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nonn,easy
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AUTHOR
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Paul D. Hanna, Jul 09 2013
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STATUS
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approved
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